Words to Equations
Help Questions
ISEE Lower Level: Quantitative Reasoning › Words to Equations
A school library starts the week with 1,200 books. On Monday, 30 books are checked out. On Tuesday, a donation of d new books arrives. On Wednesday, twice as many books are checked out as on Monday. At the end of Wednesday, the library has 1,190 books. Which equation represents the number of books in the library?
1200 - 30 + d = 1190
1200 - 30 + d - (2 * 30) = 1190
1200 + d = 1190
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 \(1200 - 30 + d - (2 \times 30) = 1190\).
Maria scored 85, 90, and x on three science tests. Her average score for the three tests was exactly 88. Which equation represents this situation?
85 + 90 + x = 88
(85 + 90) / 2 = x
(85 + 90 + x) / 3 = 88
85 + 90 = 88 + 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 \((85 + 90 + x) / 3 = 88\).
A class of 25 students is going on a trip that costs a total of $500. The students held a bake sale and raised $50, which will be used to reduce the total cost of the trip. The remaining cost will be split equally among the students. If c represents the new, lower cost for each student, which equation shows this situation?
25 + c = 500 - 50
25c = 500 - 50
25c = 500 + 50
c = 500 / 25 - 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 \(25c = 500 - 50\).
Maya has a jar of coins containing only dimes and quarters. She has 3 more quarters than she has dimes. The total value of the coins is $2.75. If d represents the number of dimes, which equation represents the total value of the coins in cents?
d + (d + 3) = 275
35(2d + 3) = 275
10d + 25(d + 3) = 275
10d + 25(d - 3) = 275
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: \(10d + 25(d + 3) = 275\).
A tank contains 200 gallons of water. A pump removes water at a rate of 5 gallons per minute, while a hose adds water at a rate of 3 gallons per minute. Which equation can be used to find m, the number of minutes it will take until the tank contains exactly 150 gallons of water?
200 / (5 - 3) = m
200 + 5m - 3m = 150
200 - (5 + 3)m = 150
200 - 5m + 3m = 150
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 \(200 - 5m + 3m = 150\).
The number of fish in a pond, 60, is 12 less than three times the number of fish, f, that were in the pond last year. Which equation correctly represents the relationship between the current and previous number of fish?
f/3 - 12 = 60
3f + 12 = 60
3f - 12 = 60
12 - 3f = 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 \(3f - 12 = 60\).
Leo bought 4 notebooks that each cost the same price and a single pen for $2. The total cost for all the items before tax was $14. If n is the price of one notebook, which equation represents the total cost of his purchase?
4n + 2 = 14
4 + n + 2 = 14
4(n + 2) = 14
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 \(4n + 2 = 14\).
A group of 4 friends buys a gift that costs $48. One friend, Amy, contributes $12 toward the cost. The remaining cost is split equally among all 4 friends. If p represents the equal amount that each of the 4 friends pays in addition to Amy's initial contribution, which equation shows this situation?
4p + 12 = 48
4p = 48 - 12
3p + 12 = 48
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 \(12 + 4p = 48\).
Five less than the product of a number x and three is the same as the number increased by nine. Which equation correctly represents this complex statement?
3x - 5 = x + 9
3(x - 5) = x + 9
5 - 3x = x + 9
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 \(3x - 5 = x + 9\).
A math puzzle says: 'I am thinking of a number, n. If you divide it by 4 and then add 7, the result is 15.' Which equation matches this puzzle?
n / (4 + 7) = 15
n/4 + 7 = 15
(n + 7) / 4 = 15
4n + 7 = 15
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.