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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
52% (02:12) correct
48%
(02:56)
wrong
based on 95
sessions
History
Date
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Not Attempted Yet
A certain French immersion summer camp whose campers are boys and girls is staffed by 20 adults. Among the campers, there are 15 girls for every 14 boys. If \(\frac{4}{9}\) of the people at the camp are boys, how many campers are there?
(A) 174
(B) 203
(C) 232
(D) 252
(E) 290
(A) 174
(B) 203
(C) 232
(D) 252
(E) 290
05 Jul 2026, 23:25
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Bookmarks
Ratio problem, and the answer choices are basically designed to bait you into answering a different question than what's asked.
1. Set up the boy/girl ratio. Girls to boys is 15 to 14, so let boys = 14k and girls = 15k. Total campers = 29k.
2. The camp also has 20 staff adults, so total people at the camp = 20 + 29k.
3. We're told boys make up 4/9 of the total people at the camp, not just of the campers, of everyone including staff. So: 14k / (20 + 29k) = 4/9.
4. Cross multiply: 9(14k) = 4(20 + 29k), which gives 126k = 80 + 116k, so 10k = 80, meaning k = 8.
5. Campers = 29k = 232.
Answer is C, 232.
Here's the trap, and it's a good one: if you solve for total people at the camp instead of campers, you get 20 + 232 = 252, which is sitting right there as answer choice D waiting for you. The question specifically asks "how many campers," not "how many people," and it's easy to lose track of that three steps into the algebra when you're just trying to get a number out.
Casual takeaway: when a ratio problem has a fixed group added on top like staff here, always double check whether the question wants that group folded into your final answer or not.
1. Set up the boy/girl ratio. Girls to boys is 15 to 14, so let boys = 14k and girls = 15k. Total campers = 29k.
2. The camp also has 20 staff adults, so total people at the camp = 20 + 29k.
3. We're told boys make up 4/9 of the total people at the camp, not just of the campers, of everyone including staff. So: 14k / (20 + 29k) = 4/9.
4. Cross multiply: 9(14k) = 4(20 + 29k), which gives 126k = 80 + 116k, so 10k = 80, meaning k = 8.
5. Campers = 29k = 232.
Answer is C, 232.
Here's the trap, and it's a good one: if you solve for total people at the camp instead of campers, you get 20 + 232 = 252, which is sitting right there as answer choice D waiting for you. The question specifically asks "how many campers," not "how many people," and it's easy to lose track of that three steps into the algebra when you're just trying to get a number out.
Casual takeaway: when a ratio problem has a fixed group added on top like staff here, always double check whether the question wants that group folded into your final answer or not.
08 Jul 2026, 11:22
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Bookmarks
Let the numbers of girl and boy campers be \(15k\) and \(14k\), respectively.
So the total number of campers is: \(14k+15k=29k\).
Including the 20 adult staff, the total number of people at the camp is: \(29k+20\).
Since \(\frac{4}{9}\) of all the people are boys:
\(\frac{14k}{29k+20}=\frac{4}{9}\).
\(9*14k=4*(29k+20)\)
\(126k=116k+80\)
\(10k=80\)
\(k=8\)
Therefore, the total number of campers is: \( 29k=29⋅8=232\).
Answer:C
So the total number of campers is: \(14k+15k=29k\).
Including the 20 adult staff, the total number of people at the camp is: \(29k+20\).
Since \(\frac{4}{9}\) of all the people are boys:
\(\frac{14k}{29k+20}=\frac{4}{9}\).
\(9*14k=4*(29k+20)\)
\(126k=116k+80\)
\(10k=80\)
\(k=8\)
Therefore, the total number of campers is: \( 29k=29⋅8=232\).
Answer:C
