Marianna's cell phone company charged her an upfront fee and a monthly fee. After three months of service, she had paid a total of $154.95. After a year of service, she had paid a total of $559.95.

Question

Her monthly fee was $______.
The upfront fee was $______.
How could one find the y-intercept (upfront fee)?

Answer 1

Let m = monthly fee
Let u = upfront fee

3m+u=154.95
u=-3m+154.95
(3 months fee + upfront fee)

12m+u=559.95
(12 months fee + upfront fee)

12m+(-3m+154.95)=559.95
9m+154.95=559.95
9m=559.95-154.95
9m=405
m=$45
(Put both equations together to find monthly fee)

3m+u=154.95
3(45)+u=154.95
135+u=154.95
u=154.95-135
u=$19.95
(Substitute the monthly fee in to find upfront fee)

Her monthly fee was $45
The upfront fee was $19.95