Question

Jake is comparing the prices of two laundry service companies. Company A charges $20 per load and an additional $8 as service charges. Company B charges $24 per load and an additional $4 as service charges. Part A: Write an equation to represent each company's total charges for cleaning a certain number of loads of laundry. For both equations (one for Company A and one for Company B), define the variable used. (4 points) Part B: Which company would charge less for 5 loads of laundry? Justify your answer. (3 points) Part C: How much money is saved by using the services of Company A instead of Company B to clean 9 loads of laundry? (3 points)

Answer 1

A.

For Company A

Let
`T_(A)` be the total charges of Company A, and let
`l` be the number of loads; we also know that the additional service charge is $8. So, putting all together into an equation we get:

`T_(A)=20l+8`

For Company B

Let
`T_(B)` be the total charges of Company B, and let
`l` be the number of loads; we also know that the additional service charge is $4. So, putting all together into an equation we get:

`T_(B)=24l+4`

Answer

Equations representing the total charges for a certain number of loads of laundry:

Company A:
`T_(A)=20l+8`

Company B:
`T_(B)=24l+4`

B.

Here we just need to replace
`l` with 5 in each equation and compare the totals.

For Company A

`T_(A)=20l+8`

`T_(A)=20(5)+8`

`T_(A)=100+8`

`T_(A)=108`

Company A charges $108 for 5 loads of laundry.

For Company B

`T_(B)=24l+4`

`T_(B)=24(5)+4`

`T_(B)=120+4`

`T_(B)=124`

Company B charges $124 for a 5 load laundry.

Answer

Company A charges less for 5 loads of laundry than Company B; in fact, Company A charges $16 less than Company B.

C.

First we are going to find how much each Company charges for 9 loads of laundry; then, we are going to subtract the total charges from Company A from the total charges of Company B.

For Company A

`T_(A)=20(9)+8`

`T_(A)=180+8`

`T_(A)=188`

Company A charges $188 for a 9 load laundry.

For Company B

`T_(B)=24l+4`

`T_(B)=24(9)+4`

`T_(B)=216+4`

`T_(B)=220`

Company B charges $220 for a 9 load laundry.

Difference: $220 - $188 = $32

Answer

Company A charges $32 than Company B to clean 9 loads of laundry.