All but 4 of the counselors at a certain summer camp have a sailing certification, first aid certification, or both. If

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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 having 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?

A) 7
B) 9
C) 11
D) 13
E) 15

Answer: D

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VJesus12 wrote:
Fri Dec 11, 2020 2:03 am
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 having 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?

A) 7
B) 9
C) 11
D) 13
E) 15

Answer: D

Solution:

We can use the formula:

Total = Sailing + First Aid - Both + Neither

We are given that Total = 22, Sailing = 7 and Neither = 4. Since we are also given that Neither is twice Both, Both = 2. Therefore, we have:

22 = 7 + First Aid - 2 + 4

22 = 9 + First Aid

13 = First Aid

Answer: D

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