Question

*please help 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.

Answer 1

Let the price for hardcover books = x

Let the price for paperback book = y

According to the statement- Adam sold 4 hardcover books and ten paperbacks and earned $64

the equation becomes

4x + 10 y = 64................ (i)

According to statement Barb sold 5 hardcover books and 7 paperbacks for the same prices each and made $58.

The equation becomes

5x + 7 y = 58...............(ii)

But as it is mentioned that Barb sold the hardcover and paperback books the same price, this gives

5x = 7y............... (iii)

x = $\frac{7y}{5}$

Now adding both equations (i) and (ii) we get

9x + 17y = 122

putting the value of x here we get

9$\frac{7y}{5} +17y = 122$

$\frac{63y}{5} +17y =122$

63y + 85y = 610

148y = 610

y = 4.121

now as x = $\frac{7y}{5}$

x = $\frac{7*4.121}{5}$ =5.769

Now we get x = 5.769  and y = 4.121

Hence, the price of hardcover book is $5.769 and paperback book is $4.121