SSAT Middle Level Quiz: Word Problems To Expressions
20 questions · exam conditions
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Word Problems To ExpressionsQuestion 1 of 20

At a fundraiser, students sell cookies for c dollars per box and waters for w dollars per bottle. They sell b boxes of cookies and d bottles of water. Which expression represents the total earnings from the fundraiser?

c∗b+w∗d\mathit{c} * \mathit{b} + \mathit{w} * \mathit{d}
c∗b+w+d\mathit{c} * \mathit{b} + \mathit{w} + \mathit{d}
c+b+w+d\mathit{c} + \mathit{b} + \mathit{w} + \mathit{d}
c∗b−w∗d\mathit{c} * \mathit{b} - \mathit{w} * \mathit{d}
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SSAT Middle Level Quiz

SSAT Middle Level Quiz: Word Problems To Expressions

Practice Word Problems To Expressions in SSAT Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Word Problems To Expressions, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

At a fundraiser, students sell cookies for c dollars per box and waters for w dollars per bottle. They sell b boxes of cookies and d bottles of water. Which expression represents the total earnings from the fundraiser?

  1. c∗b+w∗d\mathit{c} * \mathit{b} + \mathit{w} * \mathit{d} (correct answer)
  2. c∗b+w+d\mathit{c} * \mathit{b} + \mathit{w} + \mathit{d}
  3. c+b+w+d\mathit{c} + \mathit{b} + \mathit{w} + \mathit{d}
  4. c∗b−w∗d\mathit{c} * \mathit{b} - \mathit{w} * \mathit{d}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves selling cookies at c dollars per box with b boxes and waters at w dollars per bottle with d bottles, leading to the expression cb + wd. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice D is incorrect because it subtracts the water cost instead of adding it, which is a common mistake when misinterpreting total earnings. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'per' for multiplication, 'total' for addition), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 2

A class fundraiser sells bracelets for b dollars each and keychains for k dollars each. They sell x bracelets and y keychains during lunch. Which expression represents the total earnings from the fundraiser?

  1. b+x+k+y\mathit{b} + \mathit{x} + \mathit{k} + \mathit{y}
  2. b∗x−k∗y\mathit{b} * \mathit{x} - \mathit{k} * \mathit{y}
  3. b∗x+k∗y\mathit{b} * \mathit{x} + \mathit{k} * \mathit{y} (correct answer)
  4. b∗(x+k)∗y\mathit{b} * (\mathit{x} + \mathit{k}) * \mathit{y}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves selling bracelets at b dollars each with x sold and keychains at k dollars each with y sold, leading to the expression bx + ky. Choice C is correct because it accurately translates the quantities and operations described in the problem. Choice A is incorrect because it uses addition instead of multiplication for quantities and prices, which is a common mistake when overlooking per-unit costs. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'each' for multiplication), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 3

Ben makes a salad for his family dinner. He buys l heads of lettuce at a dollars each. He also buys t tomatoes at b dollars each. Then he uses a store coupon for c dollars off. What expression shows the total cost of the meal?

  1. l∗a+t∗b−c\mathit{l} * \mathit{a} + \mathit{t} * \mathit{b} - \mathit{c} (correct answer)
  2. l∗a+t∗b+c\mathit{l} * \mathit{a} + \mathit{t} * \mathit{b} + \mathit{c}
  3. l+a+t+b−c\mathit{l} + \mathit{a} + \mathit{t} + \mathit{b} - \mathit{c}
  4. l∗(a+t)∗b−c\mathit{l} * (\mathit{a} + \mathit{t}) * \mathit{b} - \mathit{c}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves buying l heads of lettuce at a dollars each, t tomatoes at b dollars each, and subtracting a coupon of c dollars, leading to the expression la + tb - c. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice B is incorrect because it adds the coupon instead of subtracting it, which is a common mistake when misreading discounts. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'each' for multiplication, 'off' for subtraction), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 4

Riley cooks pasta and buys ingredients for dinner. She buys n boxes of noodles at x dollars each. She also buys j jars of sauce at y dollars each. What expression shows the total cost of the meal?

  1. n∗x+j∗y\mathit{n} * \mathit{x} + \mathit{j} * \mathit{y} (correct answer)
  2. n+x+j+y\mathit{n} + \mathit{x} + \mathit{j} + \mathit{y}
  3. n∗x−j∗y\mathit{n} * \mathit{x} - \mathit{j} * \mathit{y}
  4. n∗(x+j)∗y\mathit{n} * (\mathit{x} + \mathit{j}) * \mathit{y}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves buying n boxes of noodles at x dollars each and j jars of sauce at y dollars each, leading to the expression nx + jy. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice C is incorrect because it subtracts the sauce cost instead of adding it, which is a common mistake when misinterpreting total costs. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'each' for multiplication), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 5

Olivia buys g packs of gum that cost m dollars each. She also buys 5 bottles of water that cost w dollars each. Then she adds a tax of t dollars to the total. Translate the word problem into an algebraic expression.

  1. g∗m+5w+t\mathit{g} * \mathit{m} + 5\mathit{w} + \mathit{t} (correct answer)
  2. g+m+5w+t\mathit{g} + \mathit{m} + 5\mathit{w} + \mathit{t}
  3. g∗m+5w−t\mathit{g} * \mathit{m} + 5\mathit{w} - \mathit{t}
  4. 5(g∗m+w)+t5(\mathit{g} * \mathit{m} + \mathit{w}) + \mathit{t}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves buying g packs of gum at m dollars each, 5 bottles of water at w dollars each, and adding tax of t dollars, leading to the expression g*m + 5w + t. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice C is incorrect because it subtracts the tax instead of adding it, which is a common mistake when confusing additions like taxes. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'each' for multiplication, 'adds' for addition), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 6

For a fundraiser, students sell raffle tickets for t dollars each and cupcakes for c dollars each. They sell r raffle tickets and u cupcakes after school. Which expression represents the total earnings from the fundraiser?

  1. t∗r+c∗u\mathit{t} * \mathit{r} + \mathit{c} * \mathit{u} (correct answer)
  2. t∗r−c∗u\mathit{t} * \mathit{r} - \mathit{c} * \mathit{u}
  3. t+r+c+u\mathit{t} + \mathit{r} + \mathit{c} + \mathit{u}
  4. t∗u+c∗r\mathit{t} * \mathit{u} + \mathit{c} * \mathit{r}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves selling tickets at t dollars each with r sold and cupcakes at c dollars each with u sold, leading to the expression tr + cu. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice D is incorrect because it switches the prices and quantities, which is a common mistake when misassigning variables. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'each' for multiplication, 'total' for addition), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 7

Troy travels in a car at c miles per hour for t hours to visit family. Then he rides a ferry at f miles per hour for h hours. How would you write an expression to represent the total distance traveled?

  1. c∗t+f∗h\mathit{c} * \mathit{t} + \mathit{f} * \mathit{h} (correct answer)
  2. c+t+f+h\mathit{c} + \mathit{t} + \mathit{f} + \mathit{h}
  3. c/t+f/h\mathit{c} / \mathit{t} + \mathit{f} / \mathit{h}
  4. c∗(t+f)∗h\mathit{c} * (\mathit{t} + \mathit{f}) * \mathit{h}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves traveling by car at c miles per hour for t hours and by ferry at f miles per hour for h hours, leading to the expression ct + fh. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice C is incorrect because it uses division instead of multiplication, which is a common mistake when confusing distance calculations. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'per' for multiplication), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 8

Kai rides a bus at b miles per hour for t hours to a museum. Later, he rides a train at r miles per hour for h hours back home. How would you write an expression to represent the total distance traveled?

  1. b∗t+r∗h\mathit{b} * \mathit{t} + \mathit{r} * \mathit{h} (correct answer)
  2. b+t+r+h\mathit{b} + \mathit{t} + \mathit{r} + \mathit{h}
  3. b/t+r/h\mathit{b} / \mathit{t} + \mathit{r} / \mathit{h}
  4. b∗(t+r)∗h\mathit{b} * (\mathit{t} + \mathit{r}) * \mathit{h}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves riding a bus at b miles per hour for t hours and a train at r miles per hour for h hours, leading to the expression bt + rh. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice C is incorrect because it uses division instead of multiplication, which is a common mistake when inverting distance formulas. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'per' for multiplication), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 9

Miles skateboards at v miles per hour for t hours on a trail. Then he rests and later skates at u miles per hour for h hours. How would you write an expression to represent the total distance traveled?

  1. v∗t+u∗h\mathit{v} * \mathit{t} + \mathit{u} * \mathit{h} (correct answer)
  2. v+t+u+h\mathit{v} + \mathit{t} + \mathit{u} + \mathit{h}
  3. v/t+u/h\mathit{v} / \mathit{t} + \mathit{u} / \mathit{h}
  4. v∗(t+u)+h\mathit{v} * (\mathit{t} + \mathit{u}) + \mathit{h}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves skateboarding at v miles per hour for t hours and later at u miles per hour for h hours, leading to the expression vt + uh. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice C is incorrect because it uses division instead of multiplication for distance, which is a common mistake when misunderstanding rate-time relationships. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'per' for multiplication), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 10

Leah makes tacos and buys ingredients at the market. She buys m pounds of meat at p dollars per pound. She also buys s bags of shredded cheese at c dollars per bag. What expression shows the total cost of the meal?

  1. m∗p+s∗c\mathit{m} * \mathit{p} + \mathit{s} * \mathit{c} (correct answer)
  2. m+p+s+c\mathit{m} + \mathit{p} + \mathit{s} + \mathit{c}
  3. m∗(p+s)+c\mathit{m} * (\mathit{p} + \mathit{s}) + \mathit{c}
  4. m∗p−s∗c\mathit{m} * \mathit{p} - \mathit{s} * \mathit{c}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves buying m pounds of meat at p dollars per pound and s bags of cheese at c dollars per bag, leading to the expression mp + sc. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice B is incorrect because it uses addition of all variables instead of multiplication for per-unit costs, which is a common mistake when ignoring rates. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'per' for multiplication), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 11

Harper buys 2 graphic novels that each cost g dollars at a book fair. She also buys m mystery books that each cost b dollars. Then she adds a donation of d dollars to support the library. What is the algebraic expression for the total cost of the items?

  1. 2g+m∗b+d2\mathit{g} + \mathit{m} * \mathit{b} + \mathit{d} (correct answer)
  2. 2g+m+b+d2\mathit{g} + \mathit{m} + \mathit{b} + \mathit{d}
  3. 2g−m∗b+d2\mathit{g} - \mathit{m} * \mathit{b} + \mathit{d}
  4. 2(g+m)∗b+d2(\mathit{g} + \mathit{m}) * \mathit{b} + \mathit{d}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves buying 2 graphic novels at g dollars each, m mystery books at b dollars each, and adding a donation of d dollars, leading to the expression 2g + m*b + d. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice C is incorrect because it subtracts the book cost instead of adding it, which is a common mistake when misinterpreting totals. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'each' for multiplication, 'adds' for addition), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 12

Maria has some stickers. She gives away 8 stickers and then buys 3 packs of stickers, with each pack containing nn stickers. If she ends up with 25 stickers, which expression represents the number of stickers Maria had originally?

  1. 25+8−3n25 + 8 - 3n (correct answer)
  2. 25−8+3n25 - 8 + 3n
  3. 25+8+3n25 + 8 + 3n
  4. 25−8−3n25 - 8 - 3n
  5. 8+3n−258 + 3n - 25
Explanation: When you encounter word problems involving multiple steps and unknown quantities, the key strategy is to work backwards from the final result to find what you started with. Let's trace Maria's sticker journey in reverse. She ends with 25 stickers. Before that final count, she had bought 3 packs of nn stickers each, adding 3n3n stickers to her collection. So before buying those packs, she must have had 25−3n25 - 3n stickers. Going further back, she had given away 8 stickers before buying the packs. If she had 25−3n25 - 3n stickers after giving away 8, then originally she must have had 25−3n+825 - 3n + 8 stickers. Rearranging this expression gives us 25+8−3n25 + 8 - 3n, which matches choice A. Let's examine why the other options don't work. Choice B (25−8+3n25 - 8 + 3n) incorrectly adds the packs she bought instead of subtracting them when working backwards. Choice C (25+8+3n25 + 8 + 3n) makes the mistake of adding both the given-away stickers and the bought packs, as if both increased her original amount. Choice D (25−8−3n25 - 8 - 3n) subtracts both quantities, which would mean she somehow started with fewer stickers than she ended with despite buying more. Remember this backwards-working technique: when a word problem describes a sequence of changes leading to a final amount, reverse each operation to find the starting point. Additions become subtractions, and subtractions become additions.

Question 13

A rectangular garden has a length that is 4 feet more than twice its width. If the width is ww feet, which expression represents the perimeter of the garden?

  1. 6w+86w + 8 (correct answer)
  2. 4w+84w + 8
  3. 3w+43w + 4
  4. 2w+82w + 8
  5. 6w+46w + 4
Explanation: When you encounter a word problem involving perimeter, you need to translate the given relationships into algebraic expressions, then apply the perimeter formula. Let's break down the given information: the width is ww feet, and the length is "4 feet more than twice the width." This means length = 2w+42w + 4 feet. For a rectangle, perimeter equals twice the length plus twice the width: P=2l+2wP = 2l + 2w. Substituting our expressions: P=2(2w+4)+2w=4w+8+2w=6w+8P = 2(2w + 4) + 2w = 4w + 8 + 2w = 6w + 8. Looking at the wrong answers: Choice B (4w+84w + 8) results from forgetting to include the width in the perimeter calculation—this would happen if you only calculated 2(2w+4)2(2w + 4) and stopped there. Choice C (3w+43w + 4) occurs if you add the length and width once instead of doubling both: (2w+4)+w=3w+4(2w + 4) + w = 3w + 4. Choice D (2w+82w + 8) comes from only doubling the length: 2(2w+4)=4w+82(2w + 4) = 4w + 8, but then incorrectly simplifying to 2w+82w + 8. The correct answer is A: 6w+86w + 8. Study tip: Always write out what each variable represents before diving into calculations. In perimeter problems, remember that you need to account for all four sides of a rectangle, which means doubling both the length and width measurements.

Question 14

A theater has ss sections, and each section has the same number of rows. If there are 3 more rows than sections, and each row has 12 seats, which expression represents the total number of seats in the theater?

  1. 12s(s+3)12s(s + 3) (correct answer)
  2. 12(s+3)12(s + 3)
  3. s(s+3)+12s(s + 3) + 12
  4. 12s+312s + 3
  5. 12s+3612s + 36
Explanation: When you encounter word problems involving multiple variables and relationships, your key strategy is to identify each quantity step-by-step and build the expression methodically. Let's break down what we know: The theater has ss sections, each section has the same number of rows, there are 3 more rows than sections, and each row contains 12 seats. Since there are 3 more rows than sections, the number of rows per section is (s+3)(s + 3). To find the total number of seats, we need: (number of sections) × (rows per section) × (seats per row) = s×(s+3)×12=12s(s+3)s \times (s + 3) \times 12 = 12s(s + 3). Looking at the wrong answers: Choice B, 12(s+3)12(s + 3), calculates the seats in just one section rather than all ss sections—it's missing the multiplication by ss. Choice C, s(s+3)+12s(s + 3) + 12, gives you the total number of rows plus 12, but forgets to multiply by 12 seats per row entirely. Choice D, 12s+312s + 3, incorrectly adds 3 to the product of 12 and ss, which doesn't represent any meaningful quantity in this context. The correct answer is A: 12s(s+3)12s(s + 3). Study tip: In multi-step word problems, always identify what each variable represents and write out the relationship in words before building your algebraic expression. Watch for problems where you need to multiply three quantities together—these often appear on the SSAT quantitative section.

Question 15

A swimming pool is being filled with water. Initially, it contains 500 gallons. Water flows in at a rate of 25 gallons per minute for tt minutes, but due to a small leak, 2 gallons per minute flow out. Which expression represents the amount of water in the pool after tt minutes?

  1. 500+25t500 + 25t
  2. 500+23t500 + 23t (correct answer)
  3. 500+27t500 + 27t
  4. 525t−2t525t - 2t
  5. 500−23t500 - 23t
Explanation: This is a rate problem where you need to track water flowing both in and out of the pool simultaneously. When dealing with rates in opposite directions, you always combine them by finding the net rate. Start with what you know: the pool begins with 500 gallons. Water flows in at 25 gallons per minute, but 2 gallons per minute leak out. The net rate of water entering the pool is 25−2=2325 - 2 = 23 gallons per minute. After tt minutes, the total amount of water added will be 23t23t gallons. Adding this to the initial 500 gallons gives you 500+23t500 + 23t, which is answer choice B. Let's examine why the other options are incorrect. Choice A (500+25t500 + 25t) only accounts for the water flowing in and completely ignores the leak—a common oversight when students focus on just one part of the problem. Choice C (500+27t500 + 27t) makes the error of adding the inflow and outflow rates instead of subtracting them, treating both as if they increase the water level. Choice D (525t−2t525t - 2t) incorrectly treats the initial 500 gallons as a rate rather than a starting amount, and it doesn't properly represent how the rates combine over time. Study tip: In rate problems involving opposite directions (filling vs. draining, moving toward vs. away from), always identify the net rate first. Look for keywords like "flows out," "leaks," or "drains" that signal you need to subtract rates rather than add them.

Question 16

Tom has a collection of baseball cards. He gives 13\frac{1}{3} of his cards to his brother and then buys 12 more cards. If he originally had cc cards, which expression represents the number of cards he has now?

  1. 2c3+12\frac{2c}{3} + 12 (correct answer)
  2. c3+12\frac{c}{3} + 12
  3. c−13+12c - \frac{1}{3} + 12
  4. c+123\frac{c + 12}{3}
  5. 2c+123\frac{2c + 12}{3}
Explanation: When you encounter word problems involving fractions and operations, the key is to translate each step of the story into mathematical expressions, working in the order events happen. Let's trace through Tom's card collection step by step. Tom starts with cc cards. First, he gives away 13\frac{1}{3} of his cards to his brother. This means he gives away 13⋅c=c3\frac{1}{3} \cdot c = \frac{c}{3} cards. After giving these away, he has c−c3c - \frac{c}{3} cards remaining. To simplify this, think of cc as 3c3\frac{3c}{3}, so c−c3=3c3−c3=2c3c - \frac{c}{3} = \frac{3c}{3} - \frac{c}{3} = \frac{2c}{3} cards. Next, Tom buys 12 more cards. Adding these to what he already has: 2c3+12\frac{2c}{3} + 12. This matches choice A. Choice B (c3+12\frac{c}{3} + 12) represents only the cards Tom gave away plus 12, ignoring the cards he kept. Choice C (c−13+12c - \frac{1}{3} + 12) incorrectly subtracts just 13\frac{1}{3} instead of 13\frac{1}{3} of his total cards—this treats the fraction as a fixed number rather than a fraction of cc. Choice D (c+123\frac{c + 12}{3}) suggests he somehow divided his final total by 3, which doesn't match the story at all. Study tip: In fraction word problems, always convert "giving away a fraction" into subtraction: if you give away 13\frac{1}{3}, you keep 23\frac{2}{3}. Write out each step algebraically before trying to match answer choices.

Question 17

A rectangular parking lot is twice as long as it is wide. If the width increases by 5 feet and the length increases by 8 feet, and the original width was ww feet, which expression represents the new area of the parking lot?

  1. 2w2+18w+402w^2 + 18w + 40 (correct answer)
  2. 2w2+13w+402w^2 + 13w + 40
  3. (w+5)(w+8)(w + 5)(w + 8)
  4. 2w+132w + 13
  5. (w+5)(2w)(w + 5)(2w)
Explanation: When you encounter word problems involving changing dimensions, you need to carefully set up expressions for both the original and new measurements, then calculate the area using length × width. Let's establish what we know: the original width is ww feet, and since the parking lot is twice as long as it is wide, the original length is 2w2w feet. After the changes, the new width becomes w+5w + 5 feet and the new length becomes 2w+82w + 8 feet. The new area equals: (w+5)(2w+8)(w + 5)(2w + 8) Using the distributive property (FOIL): (w+5)(2w+8)=w(2w)+w(8)+5(2w)+5(8)(w + 5)(2w + 8) = w(2w) + w(8) + 5(2w) + 5(8) =2w2+8w+10w+40= 2w^2 + 8w + 10w + 40 =2w2+18w+40= 2w^2 + 18w + 40 This confirms answer A is correct. Looking at the wrong answers: Answer B (2w2+13w+402w^2 + 13w + 40) results from incorrectly adding the middle terms—getting 8w+10w=13w8w + 10w = 13w instead of 18w18w. Answer C ((w+5)(w+8)(w + 5)(w + 8)) assumes both original dimensions were ww, ignoring that the length is twice the width. Answer D (2w+132w + 13) represents a perimeter-type calculation rather than area, and fails to account for the squared terms that come from multiplying length and width. Remember: when dimensions change in geometry problems, always write out the new expressions completely before multiplying. Double-check your algebra, especially when distributing—middle term errors are common on the SSAT.

Question 18

A pizza is cut into equal slices. If there are pp people and each person eats 3 slices with 4 slices remaining, which expression represents the total number of slices the pizza was cut into?

  1. 3p+43p + 4 (correct answer)
  2. p+7p + 7
  3. 3p−43p - 4
  4. 4p+34p + 3
  5. 7p7p
Explanation: When you encounter word problems involving totals made up of different parts, your goal is to identify all the components and add them together to find the whole. In this pizza problem, you need to find the total number of slices. The pizza slices can be grouped into two categories: slices that were eaten and slices that remain uneaten. Since there are pp people and each person eats 3 slices, the total slices eaten equals 3p3p. Additionally, 4 slices remain uneaten. Therefore, the total number of slices is 3p+43p + 4. Let's examine why each answer choice works or doesn't work: Choice A (3p+43p + 4) correctly adds the eaten slices (3p3p) to the remaining slices (4) to get the total. Choice B (p+7p + 7) incorrectly assumes each person eats only 1 slice instead of 3, then mysteriously adds 7 instead of the 4 remaining slices. Choice C (3p−43p - 4) makes the error of subtracting the remaining slices from the eaten slices. This would give you fewer slices than were actually eaten, which makes no sense for a total. Choice D (4p+34p + 3) confuses the given information by assuming each person eats 4 slices with 3 remaining, which reverses the actual numbers. Study tip: In "total" problems, always identify what makes up the whole. Draw a simple equation: Total = Part 1 + Part 2 + ... + Part n. This prevents you from accidentally subtracting components or mixing up the given numbers.

Question 19

Sofia buys 3 shirts that each cost s dollars at the mall. She also buys p pairs of socks that each cost d dollars. Then she subtracts a discount of k dollars from her total. What is the algebraic expression for the total cost of the items?

  1. 3s+p∗d−k3\mathit{s} + \mathit{p} * \mathit{d} - \mathit{k} (correct answer)
  2. 3s+p+d−k3\mathit{s} + \mathit{p} + \mathit{d} - \mathit{k}
  3. 3s−p∗d−k3\mathit{s} - \mathit{p} * \mathit{d} - \mathit{k}
  4. 3(s+p)∗d−k3(\mathit{s} + \mathit{p}) * \mathit{d} - \mathit{k}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves buying 3 shirts at s dollars each, p pairs of socks at d dollars each, and subtracting a discount of k dollars, leading to the expression 3s + p*d - k. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice C is incorrect because it subtracts the sock cost instead of adding it, which is a common mistake when misreading totals. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'each' for multiplication, 'subtracts' for subtraction), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.

Question 20

Ethan makes smoothies and buys fruit for the week. He buys a apples at p dollars each and b bananas at q dollars each. He also spends i dollars on ice once. What expression shows the total cost of the meal?

  1. a∗p+b∗q+i\mathit{a} * \mathit{p} + \mathit{b} * \mathit{q} + \mathit{i} (correct answer)
  2. a∗p+b∗q−i\mathit{a} * \mathit{p} + \mathit{b} * \mathit{q} - \mathit{i}
  3. a+p+b+q+i\mathit{a} + \mathit{p} + \mathit{b} + \mathit{q} + \mathit{i}
  4. a∗(p+b)∗q+i\mathit{a} * (\mathit{p} + \mathit{b}) * \mathit{q} + \mathit{i}
Explanation: This question tests middle school algebraic skills: translating word problems into algebraic expressions. Algebraic expressions use variables to represent quantities and operations from real-world situations. Understanding requires identifying quantities and operations in the text. In this scenario, the problem involves buying a apples at p dollars each, b bananas at q dollars each, and adding i dollars for ice, leading to the expression ap + bq + i. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice B is incorrect because it subtracts the ice cost instead of adding it, which is a common mistake when confusing one-time additions. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'each' for multiplication, 'also' for addition), practice translating simple scenarios, and verify expressions by checking against the word problem logic. Watch for: students confusing operation keywords or misidentifying variables.