George pays a flat amount for the first 200 minutes plus so much for each additional minute on his cellular phone each month. Last month it cost him $33.78 for 244 minutes of use. The previous month it cost $38.94 for 287 minutes of use. What are the flat rate and per minute charge for his phone service?
if f is the flat rate, and m the per-minute rate,
f+287m = 38.94
f+244m = 33.78
notice that an extra 43 minutes cost an extra $5.16, or $.12/min. So, now we know that
f+287(.12) = 38.94, so
f = 4.5
so, the flat rate is $4.50
To find the flat rate and per minute charge for George's phone service, we can use a system of equations.
Let's denote:
- The flat rate as "F"
- The per minute charge as "P"
- The number of minutes used in the first month as "M1" (287 minutes in this case)
- The total cost for the first month as "C1" ($38.94 in this case)
- The number of minutes used in the second month as "M2" (244 minutes in this case)
- The total cost for the second month as "C2" ($33.78 in this case)
Using the information provided, we can set up the following equations:
Equation 1: F + P * M1 = C1
Equation 2: F + P * M2 = C2
Now we can solve this system of equations to find the values of F and P.
Subtracting Equation 2 from Equation 1:
(F + P * M1) - (F + P * M2) = C1 - C2
P * M1 - P * M2 = C1 - C2
P * (M1 - M2) = C1 - C2
P = (C1 - C2) / (M1 - M2)
Using the given values, we can substitute them into the equation:
P = ($38.94 - $33.78) / (287 - 244)
P = $5.16 / 43
P ≈ $0.12 (rounded to two decimal places)
Now we can substitute the value of P back into Equation 1 to solve for F:
F + P * M1 = C1
F + $0.12 * 287 = $38.94
F + $34.44 = $38.94
F = $38.94 - $34.44
F ≈ $4.50 (rounded to two decimal places)
Therefore, the flat rate for George's phone service is approximately $4.50, and the per minute charge is approximately $0.12.