At a bookstore, used hardcover books sell for $8 each and used softcover books sell for $2 each. You purchase 36 used books and spend $144. How many softcover books do you buy?

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At a bookstore, used hardcover books sell for $8 each and used softcover books sell for $2 each. You purchase 36 used books and spend $144. How many softcover books do you buy?

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Answer 1 · 2016-11-19T17:44:00

I bought $12$ $12$ hardcover books and $24$ $24$ softcover books.

Explanation:

We shall represent the hardcover books purchased by $x$ $x$ and the softcover books purchased by $y$ $y$ . From the details we can write two equations:

$x + y = 36$ $x+y=36$
$8 x + 2 y = 144$ $8x+2y=144$

From the first equation we can calculate the value of $y$ $y$ .

$x + y = 36$ $x+y=36$

Subtract $x$ $x$ from each side.

$y = 36 - x$ $y=36-x$

Now, in the second equation, substitute $y$ $y$ with $(36 - x)$ $color(red)((36-x))$ .

$8 x + 2 y = 144$ $8x+2y=144$

$8 x + 2 (36 - x) = 144$ $8x+2color(red)((36-x))=144$

Open the brackets and simplify.

$8 x + 72 - 2 x = 144$ $8x+72-2x=144$

$6 x + 72 = 144$ $6x+72=144$

Subtract $72$ $72$ from both sides.

$6 x = 72$ $6x=72$

Divide both sides by $6$ $6$ .

$x = 12$ $x=12$

Now in the first equation, substitute $x$ $x$ with $12$ $color(red)(12)$ .

$x + y = 36$ $x+y=36$

$12 + y = 36$ $color(red)(12)+y=36$

Subtract $12$ $12$ from both sides.

$y = 24$ $y=24$

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At a bookstore, used hardcover books sell for $8 each and used softcover books sell for $2 each. You purchase 36 used books and spend $144. How many softcover books do you buy?

1 Answer

Explanation:

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