The high school band has 12 more girls than boys. The band has a total of 106 students. How many boys are in the band?

Answer 1

Number of boys = X

Number of girls = X + 12

total students = 106

X +( X + 12 ) = 106

2X + 12 = 106

-12 -12

2X = 94

X = 47 Number of boys

Answer 2

Let "g" be the number of girls in the band, and "b" be the number of boys.

We know that:

g + b = 106

We know this because the band is (presumably) made up of only girls and boys and therefor the total number of students in the band, 106, must be the sum of the total number of girls and boys. (For example: 100 girls plus 6 boys equals 106 students.)

We also know that:

g = b + 12

This is because there are 12 more girls than boys. (For example: if there are 8 boys, there would be 20 girls.)

If we substitute (b + 12) into the first equation for g, we get:

(b + 12) + b = 106

Then we do a little algebra:

b + 12 + b = 106

2b + 12 = 106

2b = 94

b = 47

This means there are 47 boys. It would then follow that there are 59 girls, since there are 12 more girls then boys (see equation 2). To check our work: 47 boys + 59 girls = 106 students.