Question

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

Answer 1

Explanation:

We can make 2 simultaneous equations and solve for the set fee

and the per minute charge:

Let x = fixed monthly rate

Let m = per minute charge

x + 100m = 135 {equation 1}

x + 500m = 375 {equation 2}

subtract equation 1 from equation 2

400m = 240

m = 0.6

substitute that back into equation 1 or 2 to solve for x.

Using equation 1

x + 100(.6) = 135

x + 60 = 135

x = 75

The fixed monthly rate is $75

The per minute charge is $0.6

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If y is the total cost for a month and x is the

number of minutes used the equation is:

y = 0.6x + 75

Answer 2

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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