If jeff bought 2 basketballs and 3 baseballs for $10 and herman bought 3 basketballs and 4 baseballs for $15, how much is a basketball. Show all work.
To find the cost of a basketball, we can set up a system of equations based on the given information.
Let's assign variables to represent the cost of a basketball and a baseball. Let's say the cost of a basketball is "b" and the cost of a baseball is "c".
Based on the given information, we can write two equations:
Equation 1: 2b + 3c = 10 (since Jeff bought 2 basketballs and 3 baseballs for $10)
Equation 2: 3b + 4c = 15 (since Herman bought 3 basketballs and 4 baseballs for $15)
Now, we can solve this system of equations to find the values of "b" and "c".
One way to solve this system is by using the method of substitution.
From Equation 1, solve for b in terms of c:
2b = 10 - 3c
b = (10 - 3c)/2
Substitute this expression for b into Equation 2:
3((10 - 3c)/2) + 4c = 15
Simplify the equation:
(30 - 9c)/2 + 4c = 15
30 - 9c + 8c = 30
Combine like terms:
-c = 0
c = 0
Substitute this value of c into Equation 1 to find the value of b:
2b + 3(0) = 10
2b = 10
b = 10/2
b = 5
Therefore, the cost of a basketball is $5.