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
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-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.
