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.
Do you have a question?
yes how can i find the y intercept?
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the upfront fee is represented by the variable 'x' and the monthly fee is represented by the variable 'y'.
From the given information, we can form two equations:
1) After three months of service: x + 3y = 154.95
2) After a year of service (12 months): x + 12y = 559.95
We now have a system of linear equations. We can solve it using various methods, such as substitution or elimination. Let's solve it using the elimination method:
To eliminate the 'x' term, we can multiply the first equation by -1:
-1(x + 3y) = -1(154.95)
- x - 3y = -154.95
Now we can add equation (2) and the new equation together:
(x + 12y) + (-x - 3y) = 559.95 + (-154.95)
12y - 3y = 405
Simplifying, we get:
9y = 405
To solve for 'y', we divide both sides by 9:
9y/9 = 405/9
y = 45
Now that we have the value of 'y', we can substitute it into one of the original equations to find 'x':
x + 3(45) = 154.95
x + 135 = 154.95
x = 154.95 - 135
x = 19.95
Therefore, the upfront fee (x) is $19.95, and the monthly fee (y) is $45.