Question

*WILL MARK BRAINLIEST*

Answer 1

Answer: Charges for  a hardcover book is  $6 and Charges for  a paperback book is  $4

Step-by-step explanation:

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