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)?
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
To find the monthly fee and upfront fee, we can set up a system of equations based on the given information.
Let's assume the monthly fee is represented by 'x' and the upfront fee is represented by 'y'.
From the given information, we can form two equations:
Equation 1: 3x + y = 154.95
Equation 2: 12x + y = 559.95
The first equation represents the total amount paid after three months, where the monthly fee is multiplied by the number of months (3) and added to the upfront fee.
The second equation represents the total amount paid after a year (12 months), where the monthly fee is multiplied by the number of months (12) and added to the upfront fee.
To find the monthly fee, we can first subtract the second equation from the first equation:
(3x + y) - (12x + y) = 154.95 - 559.95
Simplifying this equation, we get:
-9x = -405
Dividing both sides of the equation by -9, we get:
x = 45
So, the monthly fee (x) is $45.
To find the upfront fee, we can substitute the value of x into either Equation 1 or Equation 2. Let's use Equation 1:
3x + y = 154.95
3(45) + y = 154.95
135 + y = 154.95
Simplifying this equation, we get:
y = 154.95 - 135
y = 19.95
So, the upfront fee (y) is $19.95.
Therefore, the monthly fee is $45 and the upfront fee is $19.95.
To find the y-intercept (upfront fee) algebraically, we can simply use the equation we derived for the upfront fee:
y = 154.95 - 135
By evaluating this equation, we find that the y-intercept (upfront fee) is $19.95.