A survey asked whether some students went swimming (S) or played tennis (T) last month. - 17 played tennis. - 11 did not go swimming and did not play tennis. - 22 went swimming. - 8 went swimming and played tennis. Some of this information is shown on the Venn diagram below. How many students were in the survey?

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A survey asked whether some students went swimming (S) or played tennis (T) last month - OCR - GCSE Maths - Question 7 - 2019 - Paper 1

Question 7

A survey asked whether some students went swimming (S) or played tennis (T) last month. - 17 played tennis. - 11 did not go swimming and did not play tennis. - 22 w... show full transcript

Worked Solution & Example Answer:A survey asked whether some students went swimming (S) or played tennis (T) last month - OCR - GCSE Maths - Question 7 - 2019 - Paper 1

Step 1

Calculate total number of students who played tennis (T)

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Answer

From the information provided, we know that 17 students played tennis, and 8 of them also went swimming. Therefore, the number of students that only played tennis is:

$17 - 8 = 9$

So, there are 9 students who only played tennis.

Step 2

Calculate total number of students who went swimming (S)

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Answer

There are 22 students who went swimming, which includes those who also played tennis. Therefore, the number of students who only went swimming is:

$22 - 8 = 14$

So, there are 14 students who only went swimming.

Step 3

Combine all groups to find total number of students surveyed

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Answer

Now, we can sum the total number of students as follows:

Students who only played tennis: 9
Students who only went swimming: 14
Students who played both tennis and went swimming: 8
Students who did not participate in either activity: 11

Thus, the total number of students surveyed is:

$9 + 14 + 8 + 11 = 42$

Therefore, the total number of students in the survey is 42.

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A survey asked whether some students went swimming (S) or played tennis (T) last month - OCR - GCSE Maths - Question 7 - 2019 - Paper 1

Worked Solution & Example Answer:A survey asked whether some students went swimming (S) or played tennis (T) last month - OCR - GCSE Maths - Question 7 - 2019 - Paper 1

Calculate total number of students who played tennis (T)

Calculate total number of students who went swimming (S)

Combine all groups to find total number of students surveyed

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