There are 56 students in the orchestra and twice that number in the band. There are 23 boys and 24 girls in the choir. If each student only participates in one group, how many students total are there in the orchestra, the band, and the choir?

There are 214 total students in the band, orchestra, and choir altogether.

Step-by-step explanation:

Band: 112

Orchestra: 56

Choir: 23 boys 23 girls - 46 total

In the band, 112 kids.

In the orchestra, 56.

In the choir, 23+23=46 total

So, if we'd like to set up an equation to solve this and make it a little easier to understand,

We can assign variables. x, y, and z for example.

Population of the band is x, orchestra receives y, and choir receives z.

This question asks simply for a total, and makes sure to specify that these kids do not share hobbies in order to make it easier to achieve that goal. Because z (the number of kids in the orchestra) is already the combination of boys and girls, our equation to reach the answer (which we will call M for Music Kids, or money if you'd like) is simple.

x + y + z = M

In this equation, there is only one variable we have yet to uncover, so all we need to do is substitute the remaining three.

So, here's the full explanation in math terms.

band kids: x

orchestra kids: y

choir kids: z

x = 112

y = 56

z = 23 + 23 = 46

z = 46

M = ?

x + y + z = M

/ / unknown: M / /

/ / substitute known variables / /

112 + 56 + 46 = M

/ / simplify / /

M = 214

Final Answer: there are 214 total students in the band, orchestra, and choir altogether.