ISEE Lower Level Quiz: Variables In Context
20 questions · exam conditions
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Variables In ContextQuestion 1 of 20

A library has f fiction books and n non-fiction books. If the library donates 50 fiction books and buys 75 new non-fiction books, which expression represents the new total number of books in the library?

f - 50 + n + 75
f + 50 + n - 75
f + n - 50 + 75
(f + n) - 50 + 75
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ISEE Lower Level Quiz

ISEE Lower Level Quiz: Variables In Context

Practice Variables In Context 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 Variables In Context, 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

A library has f fiction books and n non-fiction books. If the library donates 50 fiction books and buys 75 new non-fiction books, which expression represents the new total number of books in the library?

  1. f - 50 + n + 75 (correct answer)
  2. f + 50 + n - 75
  3. f + n - 50 + 75
  4. (f + n) - 50 + 75
Explanation: The new number of fiction books is f−50f - 50. The new number of non-fiction books is n+75n + 75. The new total number of books is the sum of these two amounts, which is (f−50)+(n+75)(f - 50) + (n + 75). By the commutative property of addition, this is the same as f−50+n+75f - 50 + n + 75. The other options incorrectly group the operations.

Question 2

There are 4 quarts in a gallon. A family drinks g gallons of milk and 3 additional quarts of milk in one week. Which expression represents the total number of quarts of milk they drank?

  1. g + 4 + 3
  2. 4(g + 3)
  3. g/4 + 3
  4. 4g + 3 (correct answer)
Explanation: To find the total number of quarts, we must first convert the gallons to quarts. Since there are 4 quarts in a gallon, g gallons is equal to 4×g4 \times g, or 4g4g quarts. Then, we add the 3 additional quarts. The correct expression for the total number of quarts is 4g+34g + 3.

Question 3

A painter charges a flat fee of $100 plus an hourly rate for his work. The total cost for a job that takes h hours is represented by the expression 100+30h100 + 30h. What does the number 30 most likely represent in this context?

  1. The total cost of the job in dollars.
  2. The flat fee for any job in dollars.
  3. The number of hours the job takes.
  4. The cost per hour of work in dollars. (correct answer)
Explanation: In the expression 100+30h100 + 30h, the total cost is calculated by adding a fixed amount (100) to an amount that changes with the number of hours worked. The term 30h30h means that for every hour h, the cost increases by $30. Therefore, 30 represents the cost per hour, or the hourly rate.

Question 4

A box contains p pencils. The pencils are to be shared equally among 7 students, and there will be 4 pencils left over. Which equation could be used to find the number of pencils each student receives, s?

  1. p = 7s + 4 (correct answer)
  2. p = 4s + 7
  3. p = 7s - 4
  4. p = 7(s + 4)
Explanation: The total number of pencils, p, must account for the pencils given to the students and the pencils left over. If each of the 7 students receives s pencils, the total number of pencils given out is 7×s7 \times s, or 7s7s. Since there are 4 pencils left over, the original total p must be the sum of those given out and those left over: p=7s+4p = 7s + 4.

Question 5

A school cafeteria has a total of T chairs. There are 12 large tables that each have 8 chairs, and a few small tables that each have 4 chairs. If s represents the number of small tables, which equation correctly represents the total number of chairs?

  1. T = 12(8) + 4s (correct answer)
  2. T = 12s + 8(4)
  3. T = 12 + 8 + 4 + s
  4. T = (12 + 4)s + 8
Explanation: The total number of chairs, T, is the sum of the chairs at the large tables and the chairs at the small tables. The number of chairs at the 12 large tables is 12×812 \times 8. The number of chairs at the s small tables is 4×s4 \times s, or 4s4s. Adding these together gives the total: T=12(8)+4sT = 12(8) + 4s.

Question 6

Mariah starts with a full bag of c cat treats. She gives her cat 5 treats in the morning and 3 treats in the evening. Which expression shows how many treats are left in the bag at the end of one day?

  1. c - 5 + 3
  2. c + 5 - 3
  3. c - (5 + 3) (correct answer)
  4. c + (5 + 3)
Explanation: To find the number of treats left, we must subtract the total number of treats given away from the starting amount, c. The total number of treats given away is the sum of the morning treats (5) and evening treats (3), which is (5+3)(5 + 3). Therefore, the expression representing the remaining treats is c−(5+3)c - (5 + 3).

Question 7

A bakery had 200 cupcakes at the start of the day. They sold c cupcakes and threw away 8 that were dropped. Which equation would be used to find c if there were 24 cupcakes left at the end of the day?

  1. 200 - c - 8 = 24 (correct answer)
  2. 200 + c - 8 = 24
  3. 200 - c + 8 = 24
  4. c - 200 - 8 = 24
Explanation: The number of cupcakes at the end of the day is the starting amount minus the cupcakes sold and minus the cupcakes thrown away. This can be represented as: Starting Amount - Sold - Thrown Away = Left. Plugging in the numbers gives the equation 200−c−8=24200 - c - 8 = 24.

Question 8

A delivery truck starts the day with 150 packages. At the first stop, the driver delivers p packages. At the second stop, the driver picks up 12 new packages. Which expression represents the number of packages on the truck after the second stop?

  1. 150 + p + 12
  2. 150 - p + 12 (correct answer)
  3. 150 - p - 12
  4. p - 150 + 12
Explanation: The truck begins with 150 packages. Delivering p packages means subtracting p from the total, resulting in 150−p150 - p. Picking up 12 new packages means adding 12 to the new total. Therefore, the expression is 150−p+12150 - p + 12.

Question 9

Sam earns money by mowing lawns for $20 each and washing cars for $10 each. He wants to earn exactly $100. If he mows m lawns, which expression shows how many cars he must wash to reach his goal?

  1. (100 - 20m) / 10 (correct answer)
  2. 100 - 20m - 10
  3. (100 + 20m) / 10
  4. 100 / (20m + 10)
Explanation: First, calculate the money Sam earns from mowing lawns, which is (20m). The remaining money he needs to earn is 100−20m100 - 20m. Since he earns $10 for each car wash, we divide the remaining amount by 10 to find the number of cars he must wash. The correct expression is (100−20m)/10(100 - 20m) / 10.

Question 10

Jamal had m dollars in his wallet. He spent half of his money on a book and then received $5 from his friend. Which expression represents the amount of money Jamal has now?

  1. m/2 + 5 (correct answer)
  2. (m + 5) / 2
  3. m - 2 + 5
  4. 2m + 5
Explanation: First, calculate the amount of money Jamal had after buying the book. Spending half of his money means dividing his initial amount m by 2, which is m/2m/2. Then, he received $5, so we add 5 to this new amount. The correct expression is m/2+5m/2 + 5.

Question 11

A video game store sells new games for $40 and used games for $15. If a customer buys n new games and 3 used games, which expression represents the total cost of the purchase?

  1. 40 + 15 + n + 3
  2. 40n + 15(3) (correct answer)
  3. 40(3) + 15n
  4. (40 + 15)(n + 3)
Explanation: The total cost is the sum of the cost of the new games and the cost of the used games. The cost of n new games at $40 each is 40×n40 \times n, or 40n40n. The cost of 3 used games at $15 each is 15×315 \times 3. Therefore, the total cost is represented by the expression 40n+15(3)40n + 15(3).

Question 12

A phone plan costs $25 per month, plus $2 for every gigabyte of data used. If g represents the number of gigabytes used, which expression represents the total cost for 3 months?

  1. 3(25 + 2g) (correct answer)
  2. 3(25) + 2g
  3. 25 + 2(3g)
  4. 3(25g + 2)
Explanation: The cost for one month is the base fee ($25) plus the data cost (2g2g), which is represented by the expression 25+2g25 + 2g. To find the total cost for 3 months, this entire monthly cost must be multiplied by 3. The correct expression is 3(25+2g)3(25 + 2g).

Question 13

A baker made a batch of d dozen muffins. He sold 40 individual muffins. Since there are 12 muffins in a dozen, which expression represents the number of muffins left?

  1. 12d - 40 (correct answer)
  2. d - 40
  3. 12(d - 40)
  4. d/12 - 40
Explanation: First, find the total number of individual muffins the baker made. Since d represents the number of dozens, the total number of muffins is 12×d12 \times d, or 12d12d. He sold 40 muffins, so we subtract 40 from the total. The correct expression is 12d−4012d - 40.

Question 14

A group of s students is divided into 4 equal teams for a game. Two students leave before the game begins. Which expression represents the number of students on each team now?

  1. s/4 - 2
  2. (s - 2) / 4 (correct answer)
  3. s / (4 - 2)
  4. 4s - 2
Explanation: First, find the number of students remaining. If 2 students leave from the original group of s students, there are s−2s - 2 students left. This new total is then divided into 4 equal teams. Therefore, the number of students on each team is represented by (s−2)/4(s - 2) / 4.

Question 15

A bus travels at a constant speed of 55 miles per hour. If h is the number of hours the bus has been traveling, which expression represents the remaining distance to a city that is 400 miles away?

  1. 400 - 55h (correct answer)
  2. 400 + 55h
  3. 55h - 400
  4. 400 / 55h
Explanation: The distance the bus has traveled is its speed (55) multiplied by the number of hours (h), which is 55h55h. The remaining distance is the total distance (400) minus the distance already traveled. Therefore, the expression is 400−55h400 - 55h.

Question 16

A recipe calls for 3 cups of flour for every 2 cups of sugar. If a baker uses s cups of sugar, which expression represents the amount of flour needed?

  1. s + 1
  2. s - 1
  3. (3/2)s (correct answer)
  4. (2/3)s
Explanation: The ratio of flour to sugar is 3 to 2, which can be written as the fraction 3/2. This means for every 1 cup of sugar, you need 3/2 (or 1.5) cups of flour. To find the amount of flour needed for s cups of sugar, you multiply s by this ratio. The correct expression is (3/2)s(3/2)s.

Question 17

Leo is y years old. His aunt is 5 years younger than twice Leo's age. Which expression represents the aunt's age?

  1. 2(y - 5)
  2. 5 - 2y
  3. y + 2 - 5
  4. 2y - 5 (correct answer)
Explanation: First, find twice Leo's age, which is 2×y2 \times y, or 2y2y. Then, to find the aunt's age, subtract 5 from that amount. The correct expression is 2y−52y - 5.

Question 18

Ms. Davis bought b boxes of crayons. Each box contains 24 crayons. She wants to give 2 crayons to each of her 30 students. Which expression shows the number of crayons she will have left?

  1. 24b - 30(2) (correct answer)
  2. b - 30(2)
  3. 24b + 30(2)
  4. 30(2) - 24b
Explanation: First, find the total number of crayons Ms. Davis has, which is the number of boxes b times 24 crayons per box, or (24b). Next, find the number of crayons she gives away, which is 30 students times 2 crayons each, or 30(2)30(2). To find the number left, subtract the amount given away from the total amount she has: 24b−30(2)24b - 30(2).

Question 19

At a carnival, a game costs 3 tickets to play. A student starts with t tickets and plays the game 4 times. Which expression shows the number of tickets the student has left?

  1. t - 3(4) (correct answer)
  2. t + 3(4)
  3. 4t - 3
  4. t - 4 - 3
Explanation: The total number of tickets used is the cost per game (3) multiplied by the number of times played (4), which is 3×43 \times 4. To find the remaining tickets, this total must be subtracted from the starting number of tickets, t. The correct expression is t−3(4)t - 3(4).

Question 20

A rectangular field has a length of 50 meters. If the perimeter of the field is P meters, which expression can be used to find the width of the field?

  1. (P - 50) / 2
  2. P - 100
  3. (P - 100) / 2 (correct answer)
  4. P / 2 - 50
Explanation: The formula for the perimeter of a rectangle is P=2l+2wP = 2l + 2w. We know the length l is 50, so P=2(50)+2wP = 2(50) + 2w, which simplifies to P=100+2wP = 100 + 2w. To find the width w, we first subtract 100 from the perimeter: P−100=2wP - 100 = 2w. Then, we divide by 2: w=(P−100)/2w = (P - 100) / 2.