Question

Working her way through school, Liz works two part-time jobs for a total of 27 hours a weekJob A pays $6.00 per hour, and Job B pays 6.60 per hourHow many hours did she work at each job the week that she made \$170.40? (Round to two decimal places if necessary.

Answer 1

• 13 , hours worked at job A

,

• 14 , hours worked at job B

STEP - BY - SEP EXPLANATION

What to find?

Numbers of hours she worked at each job.

Given:

• Total number of hours = 27

,

• Per hour pay in job A = $6

,

• Per hour pay in job B = $6.60

,

• Total amount she made = $170.40

Let x represent the number of hours she worked in job A

Let y be the number of hours she worked in job B

To solve the problem given, we will follow the steps below:

Step 1:

Set up the equation.

`x+y=27\text{ ---------------------(1)}`
`6x+6.60y=170.40-------------------(2)`

Step 2

From equation (1), make x subject of formula.

`x=27-y-----------------(3)`

Step 3

Substitute equation (3) into equation(2).

`6(27-y)+6.6y=170.40`
`162-6y+6.6y=170.40`

Step 4

Collect like - term.

`-6y+6.6y=170.40-162`
`0.6y=8.4`

Step 5

Divide both-side of the equation by 0.6

`(0.6y)/(0.6)=(8.4)/(0.6)`
`y=14`

Step 6

Determine the value of x by substituting y=14 into equation (3).

`\begin{gathered} x=27-14 \\ \\ x=13 \end{gathered}`

Therefore, she worked 13 hours in job A and 14 hours in job B.