Out of the 180 students at a summer camp, 72 signed up for canoeing. There were 23 students who signed up for trekking, and 13 of those students also signed up for canoeing.

Use a two-way table to organize the information and answer the following question:

Approximately what percentage of students signed up for neither canoeing nor trekking?

72%

40%

54%

98%

Question

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Verified Answer :

mayce777 mayce777 · Answer 1 · 2016-05-07T12:23:58-04:00

that is 72%of the kids

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RenatoMattice RenatoMattice · Answer 2 · 2019-05-22T04:43:16-04:00

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

Total number of students = 180

Number of students who signed for canoeing (C) = 72

Number of students who signed for trekking (T) = 23

Number of student who signed for trekking is also signed for canoeing = 13

Number of students who only signed for canoeing (C) = 72-13=59

Number of students who only signed for trekking (T) = 23-13=10

So, Number of students who signed up either for canoeing or trekking is given by

\(n(C\cup T)=n(C)+n(T)-n(C\cap T)\\\ (C\cup T)=72+23-13\\\ (C\cup T)=95-13\\\ (C\cup T)=82\)

So, Number of students who signed up neither for canoeing not trekking is given by

\(n(C\cup T)'=n(U)-n(C\cup T)\\\ (C\cup T)'=180-82\\\ (C\cup T)'=98\)

So, Percentage of students signed up for neither canoeing nor trekking is given by

\(\dfrac{98}{180}\times 100\\\\=54.4\%\\\\\approx 54\%\)

Hence, Third option is correct.