Joe has been keeping track of his cellular phone bills for the last two months. The bill for the first mont was $38.00 for 100 minutes of usage. The bill for the second month was$45.50 for 150 minutes of usage. Find a linear equation that gives the total monthly bill based on the minutes of usage

The problem here is that you need to find what is the monthly fee for the telephone + the fee per minute.

Data we are looking for:

x - subscription plan
y - rate per minute

1. Finding the monthly fee (x) + rate per minute (y)

x + 150y = 45.50
x + 100y = 38.00
you have to deduct those equatations (x - x = 0, 150y - 100y = 50y, 45.5 - 38 = 7.5)

- finding rate per minute:
50y = 7.50
5y = 0.75
y = 0.15

- finding monthly fee
x + 150 *0.15 = 45.50
x = 45.50 - 22.50
x = 23.00

Looking at the data above you can see that no matter for how many minutes you use your phone you have to pay 23$. For every minute you spend talking the fee is 0.15$

That is why (z) the total amount you have to pay consist of 23 (subscription) + 0.15y (15c per minute):

z = 23 + 0.15y

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