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

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.

Answer 2

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