Adam and barb had a used book sale over the weekend. adam sold 4 hardcover books and ten paperbacks and earned $64 for his efforts. barb sold 5 hardcover books and 7 paperbacks for the same prices each. barb made $58. adam and barb both charged the same price for the hardcover books and the same price for the paperbacks. how much did they charge for hardcovers and how much for paperbacks? show your work.

Let us suppose they charge $x for hardcover books and $y for  paperbacks..

According to question:

4x+10y=641 and

5x+7y=582

We have a linear equations with two variables.We can use Elimination method to solve for x and y.Multiplying equation 1 by 5 and equation 2 by 4 we have:

20x+50y=320.

10x+28y=232

-       -      -

22y =88

Dividing both sides by 22 y=4.

we replace variable y in the first equation :

4x+10*4=64

4x+40=64.

Subtracting 40 both sides:

4x=24

Dividing by 4 both sides x=6.

Total charge for hardcovers is 5x+4x=9x=9x6=$54.

Total charge for paperbacks is =7y+10y=17y=17(4)=$68.