Word Problems to Expressions

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SSAT Middle Level: Quantitative › Word Problems to Expressions

Questions 1 - 10
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?

$\mathit{c} + \mathit{b} + \mathit{w} + \mathit{d}$

$\mathit{c} * \mathit{b} + \mathit{w} * \mathit{d}$

$\mathit{c} * \mathit{b} + \mathit{w} + \mathit{d}$

$\mathit{c} * \mathit{b} - \mathit{w} * \mathit{d}$

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.

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?

$\mathit{b} * \mathit{x} + \mathit{k} * \mathit{y}$

$\mathit{b} * (\mathit{x} + \mathit{k}) * \mathit{y}$

$\mathit{b} * \mathit{x} - \mathit{k} * \mathit{y}$

$\mathit{b} + \mathit{x} + \mathit{k} + \mathit{y}$

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.

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?

$\mathit{l} * (\mathit{a} + \mathit{t}) * \mathit{b} - \mathit{c}$

$\mathit{l} + \mathit{a} + \mathit{t} + \mathit{b} - \mathit{c}$

$\mathit{l} * \mathit{a} + \mathit{t} * \mathit{b} - \mathit{c}$

$\mathit{l} * \mathit{a} + \mathit{t} * \mathit{b} + \mathit{c}$

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.

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?

$\mathit{n} + \mathit{x} + \mathit{j} + \mathit{y}$

$\mathit{n} * (\mathit{x} + \mathit{j}) * \mathit{y}$

$\mathit{n} * \mathit{x} + \mathit{j} * \mathit{y}$

$\mathit{n} * \mathit{x} - \mathit{j} * \mathit{y}$

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.

5

Jordan travels by bike at s miles per hour for t hours. After that, Jordan walks at w miles per hour for h hours. How would you write an expression to represent the total distance traveled?

$\mathit{s} / \mathit{t} + \mathit{w} / \mathit{h}$

$(\mathit{s} + \mathit{t}) + (\mathit{w} + \mathit{h})$

$\mathit{s} * (\mathit{t} + \mathit{w}) * \mathit{h}$

$\mathit{s} * \mathit{t} + \mathit{w} * \mathit{h}$

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 biking at s miles per hour for t hours and walking at w miles per hour for h hours, leading to the expression st + wh. 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 rates and times instead of multiplication, which is a common mistake when confusing 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.

6

Noah buys x movie tickets that cost t dollars each. He also buys y snacks that cost s dollars each. Then he pays a one-time service fee of f dollars. Translate the word problem into an algebraic expression.

$\mathit{x} * (\mathit{t} + \mathit{y}) * \mathit{s} + \mathit{f}$

$\mathit{x} * \mathit{t} + \mathit{y} * \mathit{s} - \mathit{f}$

$\mathit{x} * \mathit{t} + \mathit{y} * \mathit{s} + \mathit{f}$

$\mathit{x} + \mathit{t} + \mathit{y} + \mathit{s} + \mathit{f}$

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 x tickets at t dollars each, y snacks at s dollars each, and adding a fee of f dollars, leading to the expression xt + ys + f. Choice A is correct because it accurately translates the quantities and operations described in the problem. Choice D is incorrect because it subtracts the fee instead of adding it, which is a common mistake when misreading additional costs. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., 'each' for multiplication, 'fee' 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.

7

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.

$\mathit{g} * \mathit{m} + 5\mathit{w} + \mathit{t}$

$5(\mathit{g} * \mathit{m} + \mathit{w}) + \mathit{t}$

$\mathit{g} * \mathit{m} + 5\mathit{w} - \mathit{t}$

$\mathit{g} + \mathit{m} + 5\mathit{w} + \mathit{t}$

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.

8

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?

$\mathit{t} * \mathit{r} + \mathit{c} * \mathit{u}$

$\mathit{t} + \mathit{r} + \mathit{c} + \mathit{u}$

$\mathit{t} * \mathit{r} - \mathit{c} * \mathit{u}$

$\mathit{t} * \mathit{u} + \mathit{c} * \mathit{r}$

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.

9

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?

$\mathit{c} * (\mathit{t} + \mathit{f}) * \mathit{h}$

$\mathit{c} * \mathit{t} + \mathit{f} * \mathit{h}$

$\mathit{c} + \mathit{t} + \mathit{f} + \mathit{h}$

$\mathit{c} / \mathit{t} + \mathit{f} / \mathit{h}$

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.

10

Maya buys 4 notebooks that each cost n dollars at the school store. She also buys 2 pens that each cost p dollars. Then she uses a coupon worth c dollars off her total. What is the algebraic expression for the total cost of the items?

$4\mathit{n} + \mathit{p} - \mathit{c}$

$4\mathit{n} + 2\mathit{p} + \mathit{c}$

$4\mathit{n} + 2\mathit{p} - \mathit{c}$

$4(\mathit{n} + 2\mathit{p}) - \mathit{c}$

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 4 notebooks at n dollars each, 2 pens at p dollars each, and subtracting a coupon of c dollars, leading to the expression 4n + 2p - c. Choice B is correct because it accurately translates the quantities and operations described in the problem. Choice A is incorrect because it uses addition for the coupon instead of subtraction, which is a common mistake when misinterpreting discounts as additional costs. Teaching strategies: Encourage students to identify keywords indicating operations (e.g., '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.

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