The cost of renting a van for one day includes a flat rental fee plus a charge for each mile the van is driven while it is rented. A van that is driven 200 miles costs $122. A van that is driven 189 miles costs $118.15. What is the flat rental fee?
To find the flat rental fee, we need to set up a system of equations using the given information.
Let's assign variables to the flat rental fee and the charge per mile:
Let F be the flat rental fee.
Let C be the charge per mile.
From the given information, we have two equations:
1) For a van driven 200 miles: F + 200C = $122
2) For a van driven 189 miles: F + 189C = $118.15
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the elimination method:
Multiply equation 2 by -200 to eliminate the F:
-200(F + 189C) = -200($118.15)
-200F - 37800C = -$23630
Now, subtract equation 1 from equation 3:
(-200F - 37800C) - (F + 200C) = (-$23630) - $122
-200F - 37800C - F - 200C = -$23752
-201F - 38000C = -$23752
Now we have a new equation:
-201F - 38000C = -$23752
Simplify further:
201F + 38000C = $23752
Now we have a system of equations:
F + 200C = $122
201F + 38000C = $23752
To solve this system, we can multiply the first equation by 201 and subtract it from the second equation:
(201F + 38000C) - 201(F + 200C) = $23752 - (201 * $122)
201F + 38000C - 201F - 40200C = $23752 - $24542
-2200C = -$790
Now, we can solve for C by dividing both sides by -2200:
C = -$790 / -2200
C = $0.3591 (rounded to four decimal places)
Now that we have the value of C, we can substitute it into any of the original equations to find the value of F. Let's use the first equation:
F + 200C = $122
F + 200 * $0.3591 = $122
F + $71.82 = $122
F = $122 - $71.82
F = $50.18
Therefore, the flat rental fee is $50.18.
f+200m = 122
f+189m = 118.15
Now subtract; the f's go away and you have
11m = 3.85
m = 0.35
Now, I expect you can find f, the flat fee.