Of 375 musicians some play only jazz band, some play only the marching band, some play both.If 250 play in the jazz band and 130 play in both, how many play in the marching band?
My answer is 135
If m play in marching band, then
m+250-130 = 375
m = 255
How did you arrive at 135? I can see 125, but not 135.
Anyway, the question was not "how many play only in the marching band?"
thanks steve
To determine the number of musicians who play in the marching band, we need to deduce it from the given information.
We know that there are 375 musicians in total, 250 of whom play in the jazz band. Additionally, 130 musicians play in both the jazz and marching bands.
To calculate the number of musicians who play only in the marching band, we can subtract the number of musicians in the jazz band (both exclusive and overlapping) from the total number of musicians.
Total musicians = Jazz band + Marching band - Both
375 = 250 + Marching band - 130
To isolate the number of musicians in the marching band, we can rearrange the equation:
Marching band = Total musicians - Jazz band + Both
Marching band = 375 - 250 + 130
Marching band = 255
Therefore, there are 255 musicians who play in the marching band.
To find out how many musicians play in the marching band, we can use a set theory concept called the Principle of Inclusion-Exclusion.
First, we know that 250 musicians play in the jazz band, and 130 musicians play in both the jazz band and marching band. So, out of the 250 musicians in the jazz band, 130 of them also play in the marching band.
To calculate the number of musicians in the marching band, we need to consider those who only play in the marching band. Let's call this number "x".
Now, let's use the Principle of Inclusion-Exclusion formula:
Total = Number in Jazz Band + Number in Marching Band - Number in Both
375 (Total) = 250 (Number in Jazz Band) + x (Number in Marching Band) - 130 (Number in Both)
By rearranging the equation, we can solve for x:
375 = 250 + x - 130
Simplifying the equation:
375 = x + 120
Subtracting 120 from both sides:
375 - 120 = x
255 = x
Therefore, there are 255 musicians in the marching band.