*word problem* 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 assume charge for a hardcover book = $ h

And charge for a paperback = $ p.

Adam sold 4 hardcover books and 10 paperbacks and earned $64.

So, we can setup an equation by using above statement.

4h + 10p = 64        equation(1)

Barb sold 5 hardcover books and 7 paperbacks and made $58.

So, we can setup another equation by using above statement.

5h + 7p = 58         equation(2)

Let us solve equation(1) and eqation (2) by elimination method.

Multiplying first equation by -5 and second equation by 4 and adding, we get

-20h -50p = -320

20h +28p =  232

    -22p = -88

Dividing both sides by -22, we get

-22p/-22 = -88/-22

p=4.

Plugging p=4 in first equation.

4h + 10(4) = 64

4h +40 =64

Subtracting 40 from both sides, we get

4h = 24.

Dividing both sides by 4, we get

4h/4 = 24/4

h=6.

Therefore, they charge $6 for a hardcover and $4 for a paperback.

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