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?

Question

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?

2. There were 44,000 people at a ball game in Los Angeles. The day's receipts were $369,000. How many people paid $ 13.00 for reserved seats and how many paid $6.00 for general admission?

Answer 1

1. They give two sets of information. Letting d = the daily charge, and m be the mileage charge, and c be the total charge

c = d + m*x where x miles are driven

123 = 3d + 300m
216 = 5d + 600m

Subtract the second from twice the first:

246 = 6d + 600m
216 = 5d + 600m

30 = d
so, 0.11

so,

c = 30 + 0.11x

2.

369000 = 13r + 6(44000-r)
369000 = 13r + 264000 - 6r
105000 = 7r
r = 15000 reserved seats
29000 general seats

Answer 2

To find the answers to these questions, we can set up a system of equations and solve them simultaneously.

1. Let's assume that the daily fee charged by Best Rentals is "d" dollars and the mileage fee is "m" dollars per mile.

For Barney, we know that he was charged $123.00 for 3 days and 300 miles. So, we can set up the equation:

3d + 300m = 123 ----(1)

For Mary, we know that she was charged $216.00 for 5 days and 600 miles. So, we can set up another equation:

5d + 600m = 216 ----(2)

To find the charges per day and for mileage, we need to solve this system of equations.

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution here.

From equation (1), we can express 3d as:

3d = 123 - 300m

Now, substitute this value of 3d into equation (2):

5(123 - 300m) + 600m = 216

Simplifying this equation will give us:

615 - 1500m + 600m = 216

Combine like terms:

615 - 900m = 216

Subtract 615 from both sides of the equation:

-900m = 216 - 615

-900m = -399

Divide both sides by -900:

m = -399 / -900

m = 0.443

So, the mileage fee charged by Best Rentals is approximately $0.443 per mile.

Now, let's substitute this value of m into equation (1) to find the daily fee:

3d + 300(0.443) = 123

3d + 132.9 = 123

3d = 123 - 132.9

3d = -9.9

Divide both sides by 3:

d = -9.9 / 3

d = -3.3

The daily fee charged by Best Rentals is approximately -$3.30.

Note: It is unusual to have negative fees, so it's possible that there might be an error in the given data or calculations.