Question

A professional organizer charges a $45 consultation fee, plus $20 per hour. Her competitor charges a $30 consultation fee, plus $26 per hour. a. Write a system of equations to represent the situation. b. Solve the system by substitution. For what number of hours will the total charge be the same? c. What will that charge be?

Answer 1

Part a) see the procedure

Part b)
`2.5\ hours`

Part c) The charge will be $95

Explanation:

Part a) Write a system of equations to represent the situation

Let

x ----> the number of hours

y ----> the total charge

we know that

A professional organizer

`y=20x+45` ----> equation A

Her competitor

`y=26x+30` ----> equation B

Part b) Solve the system by substitution. For what number of hours will the total charge be the same?

we have

`y=20x+45` ----> equation A

`y=26x+30` ----> equation B

substitute equation B in equation A

`26x+30=20x+45`

Solve for x

`26x-20x=45-30`

`6x=15`

`x=2.5\ hours`

Part c) What will that charge be?

For x=2.5 hours

substitute in equation A or equation B

The charge will be the same

Verify

Equation A

`y=20(2.5)+45=\$95`

Equation B

`y=26(2.5)+30=\$95`

therefore

The charge will be $95