High speed internet 8th grade MATH HELP PLESE !!!!!!

Question

Brain and michael are getting high speed internet access at the same time.Brain provider charges $60 for installation and $42.95 a month. Michael's provider has a free installation and charges $57.95 per month. After how many months will Brain and Michael have paid the same amount?

Answer 1

Let's write equations for both internet services...

 

#months=x

B=42.95x+60...Brian's monthly service plus

                        installation fee

M=57.95x........Michael's monthly service

 

Problems asks how many months will it take for them 

to pay the same amount, so we can equate the two 

expressions.

              B=M

42.95x+60=57.95x....expressions for Brian, Michael

           60x=15x........combine like terms

           15x=60

           ∴ x= 4...........divide both sides by 15

 

So it will take 4 months before each will have paid

the same.  Let's check our answer be substituting

x=4 into the expresessions for Brian and Michael...

B=42.95(4)+60=171.80+60=$231.80

M=57.95(4)=.....................=$231.80

 

Both costs are the same after 4months, our solution 

is correct.  Always check your work!

 

Answer 2

We can write formulas for the amount each person paid after x months. These will be

 

Brian = 60 + 42.95x

Michael = 0 + 57.95x

 

So for example, after 1 month Brian will have paid 102.95 for the installation and first month, while Michael will have paid only 57.95 (I put the zero in the equation to make it look like the familiar y-intercept form). We are trying the find the month at which they have paid equal amounts. Solve for x in the equation

 

60 + 42.95x = 57.95x

 

60 = (57.95 - 42.95)x

 

60 = 15x

 

x = 4

 

After four months.