A bookstore sells hardcover books for \15 each and paperback books for \10 each. A custome… — GRE General Test

A bookstore sells hardcover books for $\$15$ each and paperback books for $\$10$ each. A customer purchased a total of $12$ books and spent $\$150$ in total. Let $h$ represent the number of hardcover books purchased and $p$ represent the number of paperback books purchased. Which of the following equations correctly model this situation? Select all such equations.

$h + p = 12$ Answer
$15h + 10p = 150$ Answer
$3h + 2p = 30$ Answer
D
$10h + 15p = 150$
E
$15h + 10p = 12$

Answer

The correct equations are

h + p = 12

15h + 10p = 150

, and

3h + 2p = 30

The system of equations that models this situation requires one equation for the total count of books (

h + p = 12

) and one for the total monetary expenditure (

15h + 10p = 150

). Dividing the cost equation

15h + 10p = 150

by 5 gives another mathematically equivalent relation

3h + 2p = 30

. Thus, all three of these statements accurately represent the given conditions.

Step-by-Step Solution

Formulate the total quantity equation

h + p = 12

The total number of books bought is 12, which is the sum of hardcover books

h

and paperback books

p

Formulate the total cost equation

15h + 10p = 150

Hardcover books cost

\$15

each and paperbacks cost

\$10

each, yielding a total cost of

\$150

Simplify the total cost equation by dividing by the greatest common divisor

3h + 2p = 30

Dividing all coefficients in

15h + 10p = 150

5

produces an equivalent simplified linear equation.

Key Concept

Linear Modeling and Equivalent Equations

Estimated Time:1m 0s

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