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
