Variables in Context
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ISEE Lower Level: Quantitative Reasoning › Variables in Context
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?
m - 2 + 5
m/2 + 5
(m + 5) / 2
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 \(m/2\). Then, he received $5, so we add 5 to this new amount. The correct expression is \(m/2 + 5\).
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 + n) - 50 + 75
f + n - 50 + 75
f + 50 + n - 75
f - 50 + n + 75
Explanation
The new number of fiction books is \(f - 50\). The new number of non-fiction books is \(n + 75\). The new total number of books is the sum of these two amounts, which is \((f - 50) + (n + 75)\). By the commutative property of addition, this is the same as \(f - 50 + n + 75\). The other options incorrectly group the operations.
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?
40n + 15(3)
40(3) + 15n
(40 + 15)(n + 3)
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 \(40 \times n\), or \(40n\). The cost of 3 used games at $15 each is \(15 \times 3\). Therefore, the total cost is represented by the expression \(40n + 15(3)\).
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?
25 + 2(3g)
3(25 + 2g)
3(25g + 2)
3(25) + 2g
Explanation
The cost for one month is the base fee ($25) plus the data cost (\(2g\)), which is represented by the expression \(25 + 2g\). To find the total cost for 3 months, this entire monthly cost must be multiplied by 3. The correct expression is \(3(25 + 2g)\).
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?
g/4 + 3
g + 4 + 3
4g + 3
4(g + 3)
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 \(4 \times g\), or \(4g\) quarts. Then, we add the 3 additional quarts. The correct expression for the total number of quarts is \(4g + 3\).
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?
12d - 40
d/12 - 40
12(d - 40)
d - 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 \(12 \times d\), or \(12d\). He sold 40 muffins, so we subtract 40 from the total. The correct expression is \(12d - 40\).
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?
(s - 2) / 4
s / (4 - 2)
s/4 - 2
4s - 2
Explanation
First, find the number of students remaining. If 2 students leave from the original group of s students, there are \(s - 2\) students left. This new total is then divided into 4 equal teams. Therefore, the number of students on each team is represented by \((s - 2) / 4\).
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?
400 - 55h
400 + 55h
55h - 400
400 / 55h
Explanation
The distance the bus has traveled is its speed (55) multiplied by the number of hours (h), which is \(55h\). The remaining distance is the total distance (400) minus the distance already traveled. Therefore, the expression is \(400 - 55h\).
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 \(100 + 30h\). What does the number 30 most likely represent in this context?
The flat fee for any job in dollars.
The number of hours the job takes.
The total cost of the job in dollars.
The cost per hour of work in dollars.
Explanation
In the expression \(100 + 30h\), the total cost is calculated by adding a fixed amount (100) to an amount that changes with the number of hours worked. The term \(30h\) means that for every hour h, the cost increases by $30. Therefore, 30 represents the cost per hour, or the hourly rate.
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?
p = 7(s + 4)
p = 7s - 4
p = 7s + 4
p = 4s + 7
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 \(7 \times s\), or \(7s\). Since there are 4 pencils left over, the original total p must be the sum of those given out and those left over: \(p = 7s + 4\).