Question

At Jefferson High School, there are 45 seniors who play a sport and 60 seniors who play an instrument. There are also 28 seniors who play neither a sport nor an instrument. How many of the 120 seniors at Jefferson High School play BOTH a sport and instrument?

13

15

22

27

43

Answer 1

Begin by calculate play an instrument, play a sport, or both.
We do this by subtracting the # of students who don't play sports or instruments from the total number of students.
Total students - students who don't play anything = 120 - 28 = 92

Answer 2

That means that there are 92 students who play sports, play instruments, and play both
S=sports only, I=instrument only, B = both

The equation than becomes

92 = S + I + B

Answer 3

Now, since the total no. of seniors = 120. Adding all the quantity in the above venn diagram must give 120, i.e.

(45-x) + (60-x) +x +28 = 120

Now, find your value of x.