ISEE Lower Level Quiz: Equation From A Situation
20 questions · exam conditions
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Equation From A SituationQuestion 1 of 20

In a collection of marbles, the number of red marbles, r, is exactly double the number of blue marbles, b. Which equation correctly shows this relationship?

b=2rb = 2r
r=b+2r = b + 2
r=2br = 2b
b=r−2b = r - 2
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ISEE Lower Level Quiz

ISEE Lower Level Quiz: Equation From A Situation

Practice Equation From A Situation in ISEE Lower 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 Equation From A Situation, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower 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

In a collection of marbles, the number of red marbles, r, is exactly double the number of blue marbles, b. Which equation correctly shows this relationship?

  1. b=2rb = 2r
  2. r=b+2r = b + 2
  3. r=2br = 2b (correct answer)
  4. b=r−2b = r - 2
Explanation: The statement 'the number of red marbles, r, is exactly double the number of blue marbles, b' means you must multiply the number of blue marbles by 2 to get the number of red marbles. This translates to the equation r=2br = 2b.

Question 2

Maya is reading a book that is 350 pages long. She reads 25 pages each day. Let p be the number of pages she has left to read after d days. Which equation represents the number of pages left?

  1. p=350d−25p = 350d - 25
  2. p=25dp = 25d
  3. p=350−25dp = 350 - 25d (correct answer)
  4. d=350−25pd = 350 - 25p
Explanation: The total number of pages is 350. The number of pages read after d days is 25d25d. The number of pages left, p, is the total number of pages minus the number of pages read. This gives the equation p=350−25dp = 350 - 25d.

Question 3

The temperature in degrees Fahrenheit, F, can be found by multiplying the temperature in degrees Celsius, C, by 9, dividing the result by 5, and then adding 32. Which equation correctly represents this conversion?

  1. F=95C+32F = \frac{9}{5}C + 32 (correct answer)
  2. F=95(C+32)F = \frac{9}{5}(C + 32)
  3. F=9(C5+32)F = 9(\frac{C}{5} + 32)
  4. C=95F+32C = \frac{9}{5}F + 32
Explanation: Following the steps in order: 'multiplying the temperature in degrees Celsius, C, by 9' gives 9C9C. 'dividing the result by 5' gives 9C5\frac{9C}{5}. 'then adding 32' gives 9C5+32\frac{9C}{5} + 32. This is the value of F. The expression 9C5\frac{9C}{5} is the same as 95C\frac{9}{5}C, so the equation is F=95C+32F = \frac{9}{5}C + 32.

Question 4

Maria had $50 in her savings account. Each week, she added exactly $15. If w represents the number of weeks and A represents the total amount in her account, which equation shows the total amount after w weeks?

  1. A=50−15wA = 50 - 15w
  2. A=15+50wA = 15 + 50w
  3. A=50+15wA = 50 + 15w (correct answer)
  4. w=50+15Aw = 50 + 15A
Explanation: The total amount A starts at $50 and increases over time. The amount added is $15 per week, which is 15w15w. Therefore, the total amount is the starting amount plus the added amount: A=50+15wA = 50 + 15w.

Question 5

A soccer team buys one jersey and one pair of shorts for each of its p players. Jerseys cost $20 each and shorts cost $15 each. Let C be the total cost for all the players' uniforms. Which equation finds the total cost?

  1. C=(20+15)pC = (20 + 15)p (correct answer)
  2. C=20p+15C = 20p + 15
  3. C=20+15pC = 20 + 15p
  4. C=p+20+15C = p + 20 + 15
Explanation: First, find the cost for one player. One player needs one jersey (20)andonepairofshorts(20) and one pair of shorts (15), for a total of (20+20 + 15 = 35\). To find the total cost *C* for *p* players, multiply the cost per player by the number of players. This gives the equation C = 35p,whichisthesameas, which is the same as C = (20 + 15)p$.

Question 6

A movie theater sold adult tickets for $11 each and child tickets for $8 each. The total money collected was $950. If a is the number of adult tickets and c is the number of child tickets, which equation represents the total money collected?

  1. a+c=950a + c = 950
  2. 11a+8c=95011a + 8c = 950 (correct answer)
  3. 8a+11c=9508a + 11c = 950
  4. 19(a+c)=95019(a + c) = 950
Explanation: The total money from adult tickets is the price per ticket (11) times the number of tickets (*a*), which is \(11a\). The total money from child tickets is the price per ticket (8) times the number of tickets (c), which is 8c8c. The total money collected is the sum of these two amounts, so 11a+8c=95011a + 8c = 950.

Question 7

A cell phone plan costs $25 per month, which includes 500 text messages. For each text message over 500, there is a charge of $0.10. If a person sends t text messages in a month (t is greater than 500), which equation represents the total monthly cost, C?

  1. C=25+0.10tC = 25 + 0.10t
  2. C=25+0.10(t−500)C = 25 + 0.10(t - 500) (correct answer)
  3. C=25.10(t−500)C = 25.10(t - 500)
  4. C=25+0.10(500−t)C = 25 + 0.10(500 - t)
Explanation: The base cost is $25. The extra charge only applies to texts over 500. The number of texts that are charged extra is t−500t - 500. The cost for these extra texts is 0.10(t−500)0.10(t - 500). The total cost C is the base cost plus the extra charge: C=25+0.10(t−500)C = 25 + 0.10(t - 500).

Question 8

A baker starts the day with a 50-pound bag of flour. He uses 3 pounds of flour for each cake, c, that he bakes. If F represents the amount of flour remaining in the bag, which equation shows the amount of flour left?

  1. F=50+3cF = 50 + 3c
  2. F=3c−50F = 3c - 50
  3. c=50−3Fc = 50 - 3F
  4. F=50−3cF = 50 - 3c (correct answer)
Explanation: The initial amount of flour is 50 pounds. The amount used is 3 pounds per cake, so for c cakes, the amount used is 3c3c. The remaining flour, F, is the starting amount minus the amount used. This gives the equation F=50−3cF = 50 - 3c.

Question 9

A car starts with 15 gallons of gas in its tank. The car uses 2 gallons of gas for each hour, h, it is driven. Let G be the amount of gas remaining in the tank. Which equation represents this situation?

  1. G=15h−2G = 15h - 2
  2. G=15−2hG = 15 - 2h (correct answer)
  3. G=2h−15G = 2h - 15
  4. h=15−2Gh = 15 - 2G
Explanation: The starting amount of gas is 15 gallons. Gas is used, so the amount will decrease. The amount used is 2 gallons per hour, or 2h2h for h hours. The remaining gas, G, is the initial amount minus the amount used, which is represented by the equation G=15−2hG = 15 - 2h.

Question 10

A library has f fiction books and n non-fiction books. The number of fiction books is 150 fewer than three times the number of non-fiction books. Which equation correctly describes this relationship?

  1. f=3n−150f = 3n - 150 (correct answer)
  2. n=3f−150n = 3f - 150
  3. f=3(n−150)f = 3(n - 150)
  4. f=150−3nf = 150 - 3n
Explanation: The phrase 'three times the number of non-fiction books' translates to 3n3n. The phrase '150 fewer than' means we subtract 150 from that amount. Therefore, the number of fiction books, f, is equal to 3n−1503n - 150.

Question 11

A square garden has a side length of s feet. A fence is built around the garden, but a 3-foot section is left open for a gate. Let F be the total length of the fencing material used. Which equation represents the length of the fencing?

  1. F=s2−3F = s^2 - 3
  2. F=4s−3F = 4s - 3 (correct answer)
  3. F=4(s−3)F = 4(s - 3)
  4. F=4s+3F = 4s + 3
Explanation: The perimeter of a square is 4 times the side length, so the total perimeter is 4s4s. Since a 3-foot section is left open, the length of the fencing, F, is the perimeter minus the length of the gate. This is represented by the equation F=4s−3F = 4s - 3.

Question 12

Jamal is buying apples and bananas. Apples cost $0.75 each and bananas cost $0.50 each. He buys a apples and b bananas and spends exactly $10. Which equation represents this situation?

  1. a+b=10a + b = 10
  2. 75a+50b=1075a + 50b = 10
  3. 0.75a+0.50b=100.75a + 0.50b = 10 (correct answer)
  4. 0.50a+0.75b=100.50a + 0.75b = 10
Explanation: The total cost of the apples is the price per apple (0.75) times the number of apples (*a*), which is \(0.75a\). The total cost of the bananas is the price per banana (0.50) times the number of bananas (b), which is (0.50b). The sum of these costs is equal to the total amount spent, $10. So, the equation is 0.75a+0.50b=100.75a + 0.50b = 10.

Question 13

A pizza is cut into 12 equal slices. After a group of friends eats s slices, what fraction, F, of the whole pizza remains?

  1. F=12−sF = 12 - s
  2. F=s12F = \frac{s}{12}
  3. F=12−s12F = \frac{12 - s}{12} (correct answer)
  4. F=12sF = \frac{12}{s}
Explanation: First, find the number of slices remaining. If the pizza starts with 12 slices and s slices are eaten, there are 12−s12 - s slices left. The fraction of the pizza remaining is the number of remaining slices divided by the original total number of slices. Therefore, the fraction F is 12−s12\frac{12 - s}{12}.

Question 14

The length of a rectangle is 4 inches longer than its width, w. If the perimeter of the rectangle is P, which equation could be used to find the perimeter?

  1. P=w(w+4)P = w(w + 4)
  2. P=w+(w+4)P = w + (w+4)
  3. P=2w+4P = 2w + 4
  4. P=2w+2(w+4)P = 2w + 2(w + 4) (correct answer)
Explanation: The perimeter of a rectangle is found with the formula P=2l+2wP = 2l + 2w, where l is the length and w is the width. The problem states the length is '4 inches longer than its width, w', so l=w+4l = w + 4. Substituting this into the perimeter formula gives P=2(w+4)+2wP = 2(w + 4) + 2w, which can be written as P=2w+2(w+4)P = 2w + 2(w + 4).

Question 15

Ken is k inches tall. His brother, Leo, is l inches tall. Ken is 5 inches shorter than Leo. Which equation correctly relates their heights?

  1. l=k−5l = k - 5
  2. k+l=5k + l = 5
  3. k=l+5k = l + 5
  4. k=l−5k = l - 5 (correct answer)
Explanation: The statement 'Ken is 5 inches shorter than Leo' means that to find Ken's height, k, you must subtract 5 inches from Leo's height, l. This relationship is written as the equation k=l−5k = l - 5.

Question 16

David's age, d, is 7 years less than twice his sister Sarah's age, s. Which equation correctly represents David's age?

  1. d=2s−7d = 2s - 7 (correct answer)
  2. s=2d−7s = 2d - 7
  3. d=2(s−7)d = 2(s - 7)
  4. d=7−2sd = 7 - 2s
Explanation: The phrase 'twice his sister Sarah's age, s' translates to 2s2s. The phrase '7 years less than' means you subtract 7 from that amount. Therefore, David's age, d, is represented by the equation d=2s−7d = 2s - 7.

Question 17

On a science test, each correct answer (c) is worth 4 points, and for each question left blank (b), 1 point is deducted. Let S be the final score. Which equation represents the score?

  1. S=4c+bS = 4c + b
  2. S=c−4bS = c - 4b
  3. S=4(c−b)S = 4(c - b)
  4. S=4c−bS = 4c - b (correct answer)
Explanation: Points are earned for correct answers and deducted for blank answers. The points earned are 4c4c. The points deducted are (1b), or simply b. The total score S is the points earned minus the points deducted, so S=4c−bS = 4c - b.

Question 18

In a video game, a player scores 5 points for each gold coin (c) collected and loses 2 points for each trap (t) hit. Which equation represents the player's total score, S?

  1. S=5c+2tS = 5c + 2t
  2. S=5c−2tS = 5c - 2t (correct answer)
  3. S=2c−5tS = 2c - 5t
  4. S=c+t−7S = c + t - 7
Explanation: The points from coins are calculated by multiplying the number of coins, c, by 5 (5c5c). The points lost from traps are calculated by multiplying the number of traps, t, by 2 (2t2t). Since points are lost for traps, this amount is subtracted from the points gained. The total score S is 5c−2t5c - 2t.

Question 19

Leo has q quarters and d dimes in his piggy bank. The total number of coins is 42. Which equation represents the total value of the coins, V, in cents?

  1. q+d=42q + d = 42
  2. V=0.25q+0.10dV = 0.25q + 0.10d
  3. V=25q+10dV = 25q + 10d (correct answer)
  4. V=q+dV = q + d
Explanation: The question asks for the total value in cents. A quarter is worth 25 cents and a dime is worth 10 cents. The value of the quarters is 25q25q and the value of the dimes is 10d10d. The total value V is the sum of these values: V=25q+10dV = 25q + 10d. The information about 42 total coins is extra and does not relate to the value.

Question 20

Renting a party room costs a flat fee of $100, plus an additional $12 for each guest, g. If C is the total cost of the party, which equation represents this situation?

  1. C=12g+100C = 12g + 100 (correct answer)
  2. C=100g+12C = 100g + 12
  3. C=(100+12)gC = (100 + 12)g
  4. g=100+12Cg = 100 + 12C
Explanation: The total cost C is the sum of the fixed fee ($100) and the variable cost, which depends on the number of guests. The variable cost is $12 multiplied by the number of guests, g, or 12g12g. So, the total cost is C=100+12gC = 100 + 12g, which is the same as C=12g+100C = 12g + 100.