phoenixio wrote:
All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both. If twice as many of the counselors have neither certification as have both certifications, 7 of the counselors have a sailing certification, and there are a total of 22 counselors on staff, then how many of the counselors have a first aid certification?
The first sentence of the problem means that 4 counselors have neither sailing certification nor first aid certification. Therefore, the second sentence means 2 counselors have both, and 7 have sailing certification.
We can use the formula for overlapping sets and substitute the known values to solve for x, the number of counselors with a first aid certification:
Total = Sailing + First Aid - Both + Neither
22 = 7 + x - 2 + 4
22 = 9 + x
13 = x