There are 189 students in the band. The difference between the number of boys and the number of girls is 27. How many boys and girls each are in the band?
x + x + 27 = 189
2x = 189 - 27
2x = 162
x = 81
Thank you so much!
You're welcome.
To solve this problem, we need to set up a system of equations. Let's assume the number of boys in the band is represented by 'x,' and the number of girls is represented by 'y.'
From the given information, we know that there are 189 students in the band. Therefore, we can write the first equation as:
x + y = 189 (Equation 1)
We are also told that the difference between the number of boys and girls is 27. This can be written as:
x - y = 27 (Equation 2)
Now, we have a system of equations with two equations and two variables. We can solve this system to find the values of 'x' and 'y.'
One way to solve the system is by using the method of substitution. Let's solve Equation 1 for 'x' and substitute it into Equation 2:
x = 189 - y
Substituting this expression for 'x' into Equation 2, we get:
189 - y - y = 27
Simplifying, we have:
189 - 2y = 27
Now, we can solve this equation for 'y':
-2y = 27 - 189
-2y = -162
y = (-162)/(-2)
y = 81
We have found that the number of girls in the band is 81.
To find the number of boys, we can substitute this value of 'y' back into Equation 1:
x + 81 = 189
x = 189 - 81
x = 108
Therefore, there are 108 boys and 81 girls in the band.