ISEE Lower Level Quantitative Reasoning Quiz: Words To Equations

What this quiz covers

This quiz focuses on Words To Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Quantitative Reasoning.

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.

Question 1

1. 1200 - 30 + d - (2 * 30) = 1190 (correct answer)
2. 1200 - 30 + d = 1190
3. 1200 + d = 1190
4. 1200 - 30 - 2 + d = 1190

Explanation: Start with the initial number of books, 1,200. Subtract the books checked out on Monday (30). Add the donated books on Tuesday (d). On Wednesday, 'twice as many books...as on Monday' were checked out, which is (2 \times 30). This amount is also subtracted. The final count is 1,190. The equation showing all these changes is (1200 - 30 + d - (2 \times 30) = 1190).

Question 2

1. 85 + 90 + x = 88
2. (85 + 90 + x) / 3 = 88 (correct answer)
3. 85 + 90 = 88 + x
4. (85 + 90) / 2 = x

Explanation: To find the average of a set of numbers, you add the numbers together and then divide by the count of the numbers. In this case, the sum of Maria's three test scores is (85 + 90 + x). To find the average, this sum is divided by 3. The problem states this average is 88. Therefore, the correct equation is ((85 + 90 + x) / 3 = 88).

Question 3

1. 25c = 500 + 50
2. 25c = 500 - 50 (correct answer)
3. c = 500 / 25 - 50
4. 25 + c = 500 - 50

Explanation: The total cost of the trip is $500. The fundraiser reduces this cost by$50, so the new total cost is (500 - 50). This new total is split equally among 25 students, with each paying c. Therefore, the total amount paid by the students is (25 \times c), or 25c. The correct equation is (25c = 500 - 50).

Question 4

1. d + (d + 3) = 275
2. 10d + 25(d - 3) = 275
3. 35(2d + 3) = 275
4. 10d + 25(d + 3) = 275 (correct answer)

Explanation: The number of dimes is d. The number of quarters is '3 more than dimes', which is (d + 3). To find the total value in cents, multiply the number of each coin by its value in cents. The value of the dimes is 10d. The value of the quarters is (25(d + 3)). The total value is $2.75, which is 275 cents. The equation is the sum of the values: (10d + 25(d + 3) = 275).

Question 5

1. 200 + 5m - 3m = 150
2. 200 - 5m + 3m = 150 (correct answer)
3. 200 - (5 + 3)m = 150
4. 200 / (5 - 3) = m

Explanation: The tank starts with 200 gallons. Each minute (m), 5 gallons are removed, so we subtract 5m. At the same time, 3 gallons are added, so we add 3m. The amount of water in the tank after m minutes is the starting amount plus the changes: (200 - 5m + 3m). We want this amount to be 150 gallons. Therefore, the equation is (200 - 5m + 3m = 150).

Question 6

1. 3f + 12 = 60
2. 12 - 3f = 60
3. 3f - 12 = 60 (correct answer)
4. f/3 - 12 = 60

Explanation: The phrase 'three times the number of fish, f' translates to (3f). The phrase '12 less than' means you subtract 12 from the previous quantity. So, '12 less than three times the number of fish' is (3f - 12). This amount is equal to 60. Therefore, the correct equation is (3f - 12 = 60).

Question 7

1. 4(n + 2) = 14
2. 4n + 2 = 14 (correct answer)
3. 4 + n + 2 = 14
4. 4n - 2 = 14

Explanation: The cost of 4 notebooks at price n each is (4 \times n), or 4n. He also bought a pen for 2. The total cost is the sum of the cost of the notebooks and the cost of the pen, which is \(4n + 2\). This total is equal to 14. The correct equation is (4n + 2 = 14).

Question 8

1. 3p + 12 = 48
2. 4p = 48 - 12
3. 4p + 12 = 48 (correct answer)
4. p = (48 - 12) / 3

Explanation: The total cost of the gift is $48. The total money collected must equal this amount. Amy contributes$12. Then, each of the 4 friends contributes an additional p dollars. The total from the four friends is (4 \times p), or 4p. The sum of Amy's contribution and the friends' contribution is (12 + 4p). This total must equal the gift's cost, so (12 + 4p = 48).

Question 9

1. 5 - 3x = x + 9
2. 3(x - 5) = x + 9
3. 3x - 5 = x + 9 (correct answer)
4. 3x - 5 = 9x

Explanation: Let's break down the statement. 'The product of a number x and three' is 3x. 'Five less than' this product means we subtract 5 from it, giving (3x - 5). 'The number increased by nine' is (x + 9). 'Is the same as' means these two expressions are equal. Therefore, the equation is (3x - 5 = x + 9).

Question 10

1. (n + 7) / 4 = 15
2. 4n + 7 = 15
3. n / (4 + 7) = 15
4. n/4 + 7 = 15 (correct answer)

Explanation: The puzzle describes a sequence of operations. First, 'divide it by 4' gives (n/4). Second, 'then add 7' means you add 7 to that result: (n/4 + 7). The final result 'is 15', so the correct equation is (n/4 + 7 = 15). Choice A is incorrect because it adds before dividing.

Question 11

1. (s + 5) + (s + 25 + 5) = 55 (correct answer)
2. s + (s + 25) = 55
3. (s + 5) + (s + 25) = 55
4. s + 25 = 55 - 5

Explanation: The son's current age is s. The father's current age is (s + 25). In 5 years, the son's age will be (s + 5). In 5 years, the father's age will be his current age plus 5, which is ((s + 25) + 5). The sum of their ages in 5 years is 55. So, the equation is the sum of their future ages: ((s + 5) + (s + 25 + 5) = 55).

Question 12

1. A carpenter had a 50-foot board. He cut off a 10-foot section, then cut the remaining part into 4 equal pieces of length n.
2. A baker made 50 muffins. She gave away 4 muffins and then sold 10 muffins. She has n muffins left.
3. A girl had $50. She bought 4 identical shirts for `n` dollars each and received$10 in change. (correct answer)
4. A farmer has 50 acres. He plants n acres of corn and a section of wheat 4 times as large. He has 10 acres left unplanted.

Explanation: The equation (50 - 4n = 10) represents starting with a quantity of 50, subtracting a group of 4 equal items of size n, and having a result of 10. Story C describes paying with $50, where the cost of 4 shirts at `n` dollars each (4n) is subtracted from the 50, resulting in$10 change. This matches the equation.

Question 13

1. w(w + 5) = 50
2. w + (w + 5) = 50
3. 2w + 5 = 50
4. 2w + 2(w + 5) = 50 (correct answer)

Explanation: The width is w. The length is '5 feet longer than its width', which is (w + 5). The formula for the perimeter of a rectangle is (2 \times \text{length} + 2 \times \text{width}). Substituting the expressions for length and width gives (2(w + 5) + 2w). The total perimeter is 50, so the equation is (2w + 2(w + 5) = 50).

Question 14

1. 7h + 4h = 225
2. 7(2h) + 4h = 225
3. 7h + 4(2h) = 225 (correct answer)
4. h + 2h = 225

Explanation: The number of hardcover books is h, and their cost is (7h). The number of paperback books is 'twice as many', which is 2h. The cost of the paperback books is (4(2h)). The total cost is the sum of the cost of hardcovers and paperbacks. So, the equation is (7h + 4(2h) = 225).

Question 15

1. c / 12 = 10 - 5
2. c = 12 / 10 + 5
3. c = (12 * 10) + 5 (correct answer)
4. c = 10 * (12 + 5)

Explanation: The total number of cookies is the number of cookies packed in boxes plus the number of cookies left over. The number of cookies in the boxes is the number of boxes (10) multiplied by the number of cookies per box (12), which is (12 \times 10). There are 5 cookies left over, which are added to this total. Therefore, the total number of cookies c is given by the equation (c = (12 \times 10) + 5).

Question 16

1. 20w + 5 = 75
2. 20 + 5w = 75 (correct answer)
3. 5(w + 20) = 75
4. 20 + w + 5 = 75

Explanation: Liam begins with a starting amount of 20. He then adds a recurring amount each week. The money added after `w` weeks is \(5 \times w\), or `5w`. The total amount in the account is the starting amount plus the weekly savings, which is \(20 + 5w\). This total equals 75, so the correct equation is (20 + 5w = 75).

Question 17

1. 12 - m + 2m = 3
2. m + 2m = 12
3. 12 - (m + 2) = 3
4. 12 - m - 2m = 3 (correct answer)

Explanation: The starting number of slices is 12. The number of slices eaten must be subtracted from this total. Mark ate m slices. His friend ate 'twice as many', which is 2m slices. The total number of slices eaten is (m + 2m). The remaining slices are found by subtracting the eaten slices from the start: (12 - m - 2m). This is equal to 3. So, the equation is (12 - m - 2m = 3).

Question 18

1. Sam had $23. He bought 3 items that cost$5 each and had x dollars left.
2. Sam bought 5 t-shirts for x dollars each and used a $3 coupon, for a total of$23.
3. Sam bought 3 movie tickets for x dollars each. He also spent $5 on popcorn. His total spending was$23. (correct answer)
4. Sam had 23 cookies and gave 5 away. He split the rest equally among 3 friends, with each getting x cookies.

Explanation: Let's analyze the equation (3x + 5 = 23). It shows a quantity x being multiplied by 3, then 5 being added to the result, with a final total of 23. Story C matches this perfectly: the cost of 3 tickets at x dollars each is 3x, and adding the $5 popcorn cost gives a total of (3x + 5 = 23).

Question 19

1. j + (3j - 10) = 90 (correct answer)
2. 3j - 10 = 90
3. j + (10 - 3j) = 90
4. j + 3j + 10 = 90

Explanation: Jason collected j cans. 'Three times the number of cans Jason collected' is 3j. '10 fewer than' that amount is (3j - 10). This is the number of cans Ken collected. 'Together, they collected a total of 90' means you add Jason's cans and Ken's cans to get 90. So, the equation is (j + (3j - 10) = 90).

Question 20

1. p - (20 * 3) = 8 (correct answer)
2. p + 8 = 20 * 3
3. 20 * 3 - p = 8
4. p / 3 - 20 = 8

Explanation: The initial number of pencils is p. The number of pencils given away is the number of students (20) times the number of pencils each received (3), which is (20 \times 3). The number remaining (8) is the starting amount minus the amount given away. Therefore, the equation is (p - (20 \times 3) = 8).