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 in the band?

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81 boys and 81 girls

To solve this problem, let's set up some equations based on the given information.

Let's assume that the number of boys in the band is "x" and the number of girls is "y".

According to the problem, there are 189 students in the band:
x + y = 189 ...........................(Equation 1)

The difference between the number of boys and girls is 27:
x - y = 27 ...........................(Equation 2)

Now, we have a system of two equations with two variables. We can solve this system of equations using a method called "substitution" or "addition". I will use the substitution method to explain.

First, we can solve Equation 1 for one variable (x or y). Let's solve it for x:
x = 189 - y

Now, substitute this value of x into Equation 2:
(189 - y) - y = 27

Simplify this equation:
189 - 2y = 27

Next, move variables to one side and constants to the other side:
189 - 27 = 2y
162 = 2y

Then, divide both sides by 2:
162/2 = y
81 = y

So, there are 81 girls in the band.

Now, substitute the value of y into Equation 1:
x + 81 = 189

Simplify this equation:
x = 189 - 81
x = 108

Therefore, there are 108 boys in the band.

To summarize, there are 108 boys and 81 girls in the band.