Question

Johnston High School has a total of 82 boys and girls who play sports. If the number of boys is 16 more than twice the number of girls, how many boys play sports at this high school?

Answer 1

x: girls, y: boys

x+y=82
2x+16=y

x+(2x+16)=82
3x+16=82
x=22

2x+16=y
2(22)+16=y
44+16=y
60=y

There are 22 girls, and 60 boys.

Answer 2

Let's call the number of boys x and the number of girls y.

Since we know that x ( the number of boys), is 16 more than twice the number of girls, we can write x like this:

x = 16 + 2y

And we know that x + y = 82 (the number of all students), then we can rearrange the equation like this:

x = 82 - y --> This we can substitute for x in the first equation and solve for y. You could've also done y = 82 - x and substituted for y in the first equation but I'm just going to do this because this I think it makes things easier. So:

82 - y = 16 + 2y --> Solve for y.
66 = 3y
22 = y --> Now we know what y, so we can plug in this value in the equation x + y = 82 for y and solve for x.

x + 22 = 82 --> Solve for x
x = 60

Therefore, the number of boys (x) is 60 and the number of girls (y) is 22.