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?

3. Solve the system of equations

x + 3y = 32

-3x + 2y = 3

4. Solve the system of equations

x + y = 6

x - y = -9

5. During the 1998-1999 Little League season, the Tigers played 52 games. They won 12 more games than they lost. How many games did they win that season?

1. To determine what Best Rentals charges per day and for mileage, we can set up a system of equations based on the given information. Let's assume the daily fee is represented by 'd' and the mileage fee is represented by 'm'.

For Barney:
3d + 300m = 123

For Mary:
5d + 600m = 216

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

Multiply the first equation by 5 and the second equation by 3 to eliminate variable 'd':
15d + 1500m = 615
15d + 1800m = 648

Now, subtract the first equation from the second:
0d + 300m = 33

So, Best Rentals charges $33 for every 100 miles. To find the per-mile charge, divide $33 by 100: $0.33.

Therefore, Best Rentals charges $0.33 per mile for mileage.

2. Let's solve the problem by setting up a system of equations:

Let 'x' represent the number of people who paid $13.00 for reserved seats.
Let 'y' represent the number of people who paid $6.00 for general admission.

We have two pieces of information:
x + y = 44000 (equation 1)
13x + 6y = 369000 (equation 2)

We can solve this system of equations using substitution. Rearrange equation 1 to solve for x:
x = 44000 - y

Substitute this value of 'x' into equation 2:
13(44000 - y) + 6y = 369000

Now simplify and solve for 'y':
572000 - 13y + 6y = 369000
-7y = -203000
y = 29000

Substitute the value of 'y' back into equation 1 to solve for 'x':
x + 29000 = 44000
x = 15000

Therefore, 15,000 people paid $13.00 for reserved seats and 29,000 people paid $6.00 for general admission.

3. To solve the system of equations:

Equation 1: x + 3y = 32
Equation 2: -3x + 2y = 3

We can solve this system of equations using the method of elimination.

Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate the 'x' term:
3x + 9y = 96
-6x + 4y = 6

Now, add the two equations together:
3x + 9y + (-6x + 4y) = 96 + 6
3y = 102
y = 34

Substitute the value of 'y' back into Equation 1 to solve for 'x':
x + 3(34) = 32
x + 102 = 32
x = -70

Therefore, the solution to the system of equations is x = -70 and y = 34.

4. To solve the system of equations:

Equation 1: x + y = 6
Equation 2: x - y = -9

We can solve this system of equations using the method of addition.

Add Equation 1 and Equation 2 together:
(x + y) + (x - y) = 6 + (-9)
2x = -3
x = -3/2 = -1.5

Substitute the value of 'x' back into Equation 1 to solve for 'y':
-1.5 + y = 6
y = 6 + 1.5
y = 7.5

Therefore, the solution to the system of equations is x = -1.5 and y = 7.5.

5. Let's solve this problem using algebra.

Let's assume the number of games the Tigers lost is represented by 'y'. Since the Tigers won 12 more games than they lost, the number of games they won can be represented as 'y + 12'.

We know that in total they played 52 games, so we can set up the equation:
(y + 12) + y = 52

Simplifying the equation:
2y + 12 = 52

Subtracting 12 from both sides:
2y = 40

Dividing both sides by 2:
y = 20

Substituting this value of 'y' back into the equation 'y + 12':
20 + 12 = 32

Therefore, the Tigers won 32 games during the 1998-1999 Little League season.