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.