Question

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?

Answer 1

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

Explanation:

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

1. `x+y=36`
2. `8x+2y=144`

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

`x+y=36`

Subtract `x` from each side.

`y=36-x`

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

`8x+2y=144`

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

Open the brackets and simplify.

`8x+72-2x=144`

`6x+72=144`

Subtract `72` from both sides.

`6x=72`

Divide both sides by `6`.

`x=12`

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

`x+y=36`

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

Subtract `12` from both sides.

`y=24`