a baseball team buys 15 bats for $405. aluminum bats cost $25 and wooden bats cost $30. how many of each type did they buy? Please show work
wooden bats ---> x
aluminum bats --> 15-x
solve
25(15-x) + 30x = 405
thank you
Let's assume the baseball team bought x aluminum bats and y wooden bats.
According to the given information:
- The cost of an aluminum bat is $25.
- The cost of a wooden bat is $30.
- They bought a total of 15 bats for $405.
We can create a system of equations based on this information:
Equation 1: x + y = 15 (since they bought a total of 15 bats)
Equation 2: 25x + 30y = 405 (the total cost of the bats is $405)
To solve the system of equations, we can use substitution or elimination. Let's use the substitution method.
From Equation 1, we can express x in terms of y:
x = 15 - y
Substitute this expression for x in Equation 2:
25(15 - y) + 30y = 405
375 - 25y + 30y = 405
5y = 405 - 375
5y = 30
y = 30/5
y = 6
Now, substitute the value of y back into Equation 1 to find x:
x + 6 = 15
x = 15 - 6
x = 9
So, the baseball team bought 9 aluminum bats and 6 wooden bats.
To solve this problem, we can use a system of equations.
Let's assume the number of aluminum bats is 'x' and the number of wooden bats is 'y'.
From the given information, we can establish the following equations:
1. The total number of bats: x + y = 15
2. The cost of aluminum bats: 25x
3. The cost of wooden bats: 30y
Since the total cost of the bats is $405, we can create another equation:
4. 25x + 30y = 405
Now we have a system of equations:
Equation 1: x + y = 15
Equation 2: 25x + 30y = 405
To solve this system, we can use the substitution method or the elimination method. Let's use the elimination method in this case.
We need to multiply Equation 1 by 25 to make the coefficients of 'x' in both equations equal:
25(x + y = 15)
25x + 25y = 375
Now, subtract Equation 2 from the above equation:
25x + 30y - (25x + 25y) = 405 - 375
5y = 30
y = 30 / 5
y = 6
Substitute the value of y (6) back into Equation 1:
x + 6 = 15
x = 15 - 6
x = 9
Therefore, the number of aluminum bats (x) is 9, and the number of wooden bats (y) is 6.