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)
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
- 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: \(T_{B}=28m+15\)
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
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Company B charges $127 for cleaning 4 mattresses.
Answer
Company B charges less for cleaning 4 mattresses.
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.
