Joe has been keeping track of his cellular phone bills for the last two months. The bill for the first month 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 (3)
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
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 . F ore v ery min u t eyo u s p e n d t a l kin g t h e f ee i s 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
Add a comment if sth is not clear
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
If y is the total cost for a month and x is the
number of minutes used the equation is:
y = 0.6x + 75 ;
Joe's monthly phone bill can be modeled by the equation y = 0.15 x + 23 , where y is the total bill and x is the number of minutes used. The slope represents the cost per minute, which is $0.15, and the y-intercept represents the basic monthly fee of $23. This equation helps in predicting the phone bill based on different minute usages.
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