Question

Jake is comparing the prices of two mattress cleaning companies. Company A charges $30 per mattress and an additional $13 as service charges. Company B charges $28 per mattress and an additional $15 as service charges. Part A: Write equations to represent Company A's and Company B's total mattress cleaning charges for a certain number of mattresses. Define the variable used in the equations. (4 points) Part B: Which company would charge less for cleaning 4 mattresses? Justify your answer. (3 points) Part C: How much money is saved by using the services of Company B instead of Company A to clean 7 mattresses? (3 points)

Answer 1

part a
company A 30+13=a
company B 28+15=a
the variable equals the answer
Company A would charge $133 for 4 mattresses
and Company B would charge $127 for 4 mattresses
for seven mattresses co. A would charge $233 dollars and co. B $209
you would save $24 by going to co. B than co. B

Answer 2

A.

- For company A

Let
`T_(A)` be the total cost that company A charges, and let
`m` be the number of mattresses cleaned.

We know that Company A charges $30 per mattress and an additional $13 as service charges. so the total cost,
`T_(A)`, will be the cost for the number of mattresses cleaned,
`30m`, plus the additional service charges. Putting all the things together, we get the equation:

`T_(A)=30m+13`

- For company B

Let
`T_(B)` be the total cost that company B charges, and let
`m` be the number of mattresses cleaned.

We know that company B charges $28 per mattress and an additional $15 as service charges, so translating this into and equation we get:

`T_(B)=28m+15`

Answer

Equations that represent Company A's and Company B's total mattress cleaning charges for a certain number of mattresses:

Company A:
`T_(A)=30m+13`

Company B:
`T_(B)=28m+15`

B.

Here we just need to replace
`m` with 4 in both equations, evaluate them, and then compare the totals.

- For company A

`T_(A)=30m+13`

`T_(A)=30(4)+13`

`T_(A)=120+13`

`T_(A)=133`

Company A charges $133 for cleaning 4 mattresses.

- For company B

`T_(B)=28m+15`

`T_(B)=28(4)+15`

`T_(B)=112+15`

`T_(B)=127`

Company B charges $127 for cleaning 4 mattresses.

Answer

Company B charges less for cleaning 4 mattresses.

C.

Here we just need to replace
`m` with 7 in both equations, evaluate them, and then subtract the Company's B total cost form Company's A total cost.

- For company A

`T_(A)=30m+13`

`T_(A)=30(7)+13`

`T_(A)=210+13`

`T_(A)=223`

- For company B

`T_(B)=28m+15`

`T_(B)=28(7)+15`

`T_(B)=196+15`

`T_(B)=211`

$223 - $211 = $12

Answer

We can save $12 by using the services of company B instead of company A.