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)

For Company A

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

For Company B

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

Answer

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

Company A:

Company B:

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

For Company A

Company A charges $108 for 5 loads of laundry.

For Company B

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.

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

Company A charges $188 for a 9 load laundry.

For Company B

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.

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: