WILL MARK BRAINLIEST
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?
1. Mathematically what kind of problem is this? What skill or concept did we learn in this unit which, when applied to this problem, will allow you to solve the problem?
2. Set up the problem showing the equations you’ll use. Be sure to label or explain what your variables mean.
3. Show the math work to arrive at the answer. Write and mark your final answer. Be sure to make it clear which is hardcover and which is paperback.

thank you so much

1) This problems belongs to linear equation in two variables. From this problem , we can say that we required a pair of linear equation to solve linear equation in two variables.

2) lets create equation

let the charges for a hardcover book is represented by variable x

let the charges for a paperback book is represented by variable y

Creating equation related to Adams work

Adam sold 4 hardcover books and 10 paperback books .

So Adams earning = (4 × x ) + ( 10 × y)

⇒ 4x + 10y = 64 ------equation 1 [ given earning of Adam = 64 ]

Creating equation related to Barb work

Barb sold 5 hardcover books and 7 paperbacks for the same prices each

so Barb's earning = (5 × x ) + ( 7 × y)

⇒ 5x + 7y = 58 -------equation 2 [ given earning of Barb = 58 ]

so two equations are

4x + 10y = 64 ------equation 1 And

5x + 7y = 58 ------equation2

where variable x represents charges for a hardcover book and variable y represents charges for paperback books

3) lets solve two equation derived in step 2

4x + 10y = 64 ------equation 1 And

5x + 7y = 58 ------equation2

On multiplying equation 1 by 5 and equation 2 by 4 to make coefficient of variable x same.

5 × ( 4x + 10y = 64 )

= 20 x + 50 y = 320 ---------------equation 3

4 × ( 5x + 7y = 58 )

= 20x + 28y = 232 ----------------equation 4

subtracting equation 3 from equation 4 we get

20x - 20x +50y - 28y = 320 - 232

⇒ 22y = 88

⇒ y = 88/22 = 4

On substituting value of y in equation 1 , we get

4x + 10× 4 = 64

⇒ 4x = 64 - 40 = 24

⇒ x = 24/4 = 6

Hence charges for a hardcover book = x = $6

And charges for a paperback book = y = $4