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.
Her monthly fee was $______.
The upfront fee was $______.
How could one find the y-intercept (upfront fee) in this equation?
To find the monthly fee and the upfront fee, we can set up a system of equations using the given information.
Let's denote the monthly fee as "M" and the upfront fee as "U".
From the information given, we can form two equations:
Equation 1: M + U = 154.95
This equation represents the total amount paid after three months.
Equation 2: 12M + U = 559.95
This equation represents the total amount paid after a year.
To find the monthly fee, we can solve the system of equations. Here's one way to do it:
1. Multiply Equation 1 by 12 to eliminate the "U" term:
12(M + U) = 12 * 154.95
12M + 12U = 1859.40
2. Subtract Equation 2 from the result obtained in step 1:
(12M + 12U) - (12M + U) = 1859.40 - 559.95
11U = 1299.45
3. Solve for "U" by dividing both sides of the equation by 11:
U = 1299.45 / 11
U ≈ 118.13
So, the upfront fee (y-intercept) is approximately $118.13.
To find the monthly fee, we can substitute the value of "U" back into either Equation 1 or Equation 2. Let's substitute it into Equation 1:
M + 118.13 = 154.95
M ≈ 154.95 - 118.13
M ≈ 36.82
Therefore, the monthly fee is approximately $36.82.