Of 375 musicians at a high school, some play only in the jazz band, some play only for the marching band, and some do 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?

Question

(1 point)
Responses

120
120

130
130

125
125

255

Answer 1

To find the number of musicians in the marching band, we first need to find the total number of musicians who play in either the jazz band or the marching band. This can be found by adding the number of musicians in the jazz band (250) to the number of musicians in the marching band only.

Let x be the number of musicians in the marching band only.

Then, the total number of musicians who play in either the jazz band or the marching band is x + 250.

However, we also know that 130 musicians play in both the jazz band and the marching band. So, if we add the number of musicians in the jazz band only (250) to the number of musicians in the marching band only (x), we have to subtract the number of musicians who play in both (130) to avoid counting them twice.

Therefore, the equation becomes:

x + 250 - 130 = 375

Simplifying the equation, we have:

x + 120 = 375

Subtracting 120 from both sides, we find:

x = 255

So, 255 musicians are in the marching band.

Therefore, the correct answer is 255.