Question

Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5.

The following functions represent the rate structures of the two rental companies:

x = the number of weeks

Company A

f(x) = 15(7x)

Company B

g(x) = 100x + 5

The function h(x) = f(x) – g(x) represents the difference between the two rate structures.

Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply.

If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B.
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
If Marguerite rents for 1 week, it will cost her the same at either company.
If Marguerite rents for 1 week, it will cost her more if she rents from Company A.
h(x) = 5x – 5
h(x) = 5x + 5

Answer 1

So, let's assume that we can just plug in 2 weeks, so,
f(x)=15(7(2)) = $210
g(x)=100(2)+5 = $205

Those are for 2 weeks, now for 1 week
f(x)=15(7(1)) = $105
g(x)=100(1)+5 = $105

Notice something?
Company A has a $5 increase from Company B

So you can choose,
`If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.`

You can also choose,
`If Marguerite rents for 1 week, it will cost her the same at either company.`

Now for this last one, just plug in your variables,
h(x)=15(7(2)) - 100(2)+5 = $15 difference

Now plug it into your options,
h(x)=5(2)-5 = 5
h(x)=5(2)+5 = 15

so, your options that are chosen would be,
`If Maguerite rents for 2 weeks, it will cost her less if she rents from Company B.`
`If Maguerite rents for 1 week, it will cost her the same at either company.`
`h(x)=5x+5`

Answer 2

Thanks bro