Question

Of 375 musicians at a high school, some play only in the jazz band, some play only in the marching band, and some play in both. If 250 of them play in the jazz band, and 130 play in both, how many of the musicians are in the marching band?

Answer 1

//Find out how many only play in the jazz band, then find out how many must be in the marching band.

250 - 130 = 120 (Number that only play in jazz band)
375 - 120 = 255 (Number that play in marching band)

255 people play in the marching band, where 130 play in both and 125 play only in it.

Answer 2

The value of musicians belonging to the marching band is 255.

Given:

The number of musicians playing only Jazz is 250.

Suppose the number of musicians playing only the marching band is x.

The total number of musicians is 375.

According to the set theory the formula for two sets A and B.

n(A∪B) = n (A) + n(B) - n( A ∩ B )   .....(1)

Let us suppose set A belongs to the musicians playing only Jazz, and set B belongs to musicians in the marching band.

Now, from equation 1.

We can rewrite as below:

375 = 250 + x -130

375-250 = x -130

125 + 130 = x

x = 255

Thus, the value of musicians belonging to the marching band is 255.

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