Question

Judy worked 8 hours and Ben worked 10 hours. Their combined pay was $80. When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65. Find the hourly rate of pay for each person

Answer 1

The hourly rate of pay for:

Jude =$5 an hour

Ben = $4 an hour

Explanation:

Let x represents Judy and y represents Ben.

As per the statement:Judy worked 8 hours and Ben worked 10 hours. Their combined pay was $80.

⇒
`8x + 10y =80` ......[1]

Also, it is given that When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65.

⇒
`9x+5y=65` .....[2]

Multiply equation [2] by 2 both sides we get;

`2(9x+5y)=2 \cdot65`

18x + 10y = 130 .....[3]

Subtract [2] from [3] to eliminate y and solve for x;

18x + 10y -8x -10y = 130 -80

Simplify:

10x = 50

Divide both sides by 10 we get;

x = 5

⇒ Judy gets paid $5 an hour

Substitute value of x in [1] we get;

8(5) + 10y = 80

40 + 10y = 80

Subtract 40 from both sides we get;

40 + 10y - 40 = 80 -40

Simplify:

10 y = 40

Divide both sides by 10 we get;

y = 4

⇒Ben gets paid $4 an hour