A rental car costs a minimum charge plus a fixed charge per mile driven. One customer was charged $60 for 160 miles of use. Another customer drove 280 miles and paid $90. Write an equation relating the total cost, C (in dollars), to the miles driven, x.
Let C = ax + b,
from the data
60 = 160a + b and
90 = 280a + b
solve these two, you should get a=1/4 and b=20
then
C = (1/4)x + 20
To write the equation relating the total cost, C (in dollars), to the miles driven, x, we need to determine the minimum charge and the fixed charge per mile driven.
Let's assume that the minimum charge is represented by "m" dollars and the fixed charge per mile driven is represented by "f" dollars.
Based on the given information, we can create two equations:
For the first customer: C1 = m + 160f
For the second customer: C2 = m + 280f
We know that the first customer was charged $60 for 160 miles, so we can substitute these values into the first equation: 60 = m + 160f.
Similarly, for the second customer, who drove 280 miles and paid $90, we can substitute these values into the second equation: 90 = m + 280f.
Now we have a system of two equations:
1) 60 = m + 160f
2) 90 = m + 280f
To solve this system of equations, we can use the method of substitution or elimination.
Using the elimination method, let's multiply the first equation by 2 and subtract it from the second equation:
2) 90 = m + 280f
-2) -120 = -2m - 320f
---------------------------
-30 = -40f
By dividing both sides of -30 = -40f by -40, we get:
f = 3/4
Now, substitute the value of f = 3/4 into the first equation to solve for m:
60 = m + 160 * (3/4)
60 = m + 120
m = -60
Therefore, the equation relating the total cost, C (in dollars), to the miles driven, x is:
C = -60 + (3/4) * x