1. Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $123.00 for 3 days and 300 miles, while Mary was charged $216.00 for 5 days and 600 miles. What does Best Rental charge per day, for mileage?
break it down line by line to set up your equations.
using d for daily charge and m for mileage charge,
Barney: 3d + 300m = 123
Mary: 5d + 600m = 216
Subtract M from 2*B:
d = 30
so, m = .11
check: 3*30 + 300*.11 = 90+33 = 123
5*30 + 600*.11 = 150+66 = 216
To find out what Best Rentals charges per day and for mileage, we can set up a system of equations.
Let's denote the daily fee as "D" and the mileage fee as "M."
Based on the given information, we can create two equations:
1) $123.00 = 3D + 300M
2) $216.00 = 5D + 600M
We can solve this system of equations to find the values of D and M.
To eliminate one variable, we can multiply equation 1 by 2 and equation 2 by 3:
1) 2($123.00) = 2(3D + 300M) => $246.00 = 6D + 600M
2) 3($216.00) = 3(5D + 600M) => $648.00 = 15D + 1800M
Subtract equation 1 from equation 2:
($648.00 - $246.00) = (15D + 1800M) - (6D + 600M)
$402.00 = 9D + 1200M
Now we have a new equation:
3) $402.00 = 9D + 1200M
We can notice that equation 3 is just three times equation 1. This suggests that equation 1 was the correct equation to start with, so we can conclude that Best Rentals charges a daily fee of $3 per day.
Now we can substitute this value into equation 1 to find the mileage fee:
$123.00 = 3D + 300M
$123.00 = 3($3.00) + 300M
$123.00 = $9.00 + 300M
To isolate M, we subtract $9.00 from both sides:
$123.00 - $9.00 = 300M
$114.00 = 300M
Finally, we divide both sides by 300 to find the mileage fee:
M = $114.00 / 300
M ≈ $0.38
Therefore, Best Rentals charges $3.00 per day for rentals and approximately $0.38 per mile.
To find the daily fee and mileage fee, we will set up a system of equations using the given information.
Let's assume the daily fee is represented by 'd' and the mileage fee is represented by 'm'.
Based on the given information:
For Barney:
3d + 300m = $123.00
For Mary:
5d + 600m = $216.00
We can now solve this system of equations using any method (substitution, elimination, etc.).
First, let's solve for 'd' in terms of 'm' by isolating 'd' in the first equation:
3d = $123.00 - 300m
d = ($123.00 - 300m)/3
Now, substitute this value of 'd' in the second equation:
5(($123.00 - 300m)/3) + 600m = $216.00
Simplify the equation:
(5/3)($123.00 - 300m) + 600m = $216.00
(5/3)*$123.00 - (5/3)*300m + 600m = $216.00
$205.00 - 500m + 600m = $216.00
Combine like terms:
100m = $11.00
Divide both sides of the equation by 100:
m = $0.11
Therefore, Best Rental charges $0.11 per mile for mileage.