A boutique bookstore sells hardcover books for \25 each and paperback books for \12 each. … — GMAT

A boutique bookstore sells hardcover books for $\$25$ each and paperback books for $\$12$ each. On a certain day, the store sold a total of $85$ books and generated a total revenue of $\$1,579$ . How many hardcover books were sold on that day?

Answer: 43 hardcover books

Answer

The total number of hardcover books sold on that day is 43.

By setting up the two linear equations

h + p = 85

(quantity) and

25h + 12p = 1579

(revenue), eliminating

p

yields

13h = 559

, which gives

h = 43

Step-by-Step Solution

Define variables and construct the system of linear equations

Let

h

be the number of hardcover books and

p

be the number of paperback books. The equations are

h + p = 85

and

25h + 12p = 1579

The total quantity of items sold gives a sum equation, and the individual prices multiplied by their quantities yield the total revenue equation.

Use substitution or elimination to solve for

h

Multiplying the total books equation by 12 yields

12h + 12p = 1020

. Subtracting this from

25h + 12p = 1579

gives

13h = 559

Eliminating

p

directly isolates the variable

h

representing hardcover books.

Calculate the value of

h

h = \frac{559}{13} = 43

Dividing the remaining total revenue by the coefficient of

h

yields the precise quantity.

Key Concept

Solving two-variable systems of linear equations using elimination or substitution

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