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Here are the results of a survey of 437 people in a town - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

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Here are the results of a survey of 437 people in a town. * 62 males speak Spanish. * 153 females do not speak Spanish. * 280 people do not speak Spanish. Jeff say... show full transcript

Worked Solution & Example Answer:Here are the results of a survey of 437 people in a town - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

Step 1

Calculate the total number of females in the town

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Answer

First, we determine how many females there are in total. Since there are 437 people in the town and 280 do not speak Spanish, we can find the number of people who speak Spanish:

437280=157437 - 280 = 157

Next, we can find how many females there are. We know that 62 males speak Spanish; thus, the total number of males is:

62+(43762280)=62+95=15762 + (437 - 62 - 280) = 62 + 95 = 157

With 157 males, we can find the number of females by subtracting from the total:

437157=280437 - 157 = 280

Step 2

Determine how many females speak Spanish

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Answer

Since 153 females do not speak Spanish, we can find how many do speak Spanish by subtracting the non-Spanish speakers from the total number of females:

280153=127280 - 153 = 127

Thus, 127 females speak Spanish.

Step 3

Calculate the proportion of females who speak Spanish

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Answer

To find the proportion of females who can speak Spanish, we take the number of females who speak Spanish and divide it by the total number of females obtained earlier:

rac{127}{280}

To simplify, we can find the equivalent fraction to see if it is greater than or equal to rac{2}{5}:

rac{127 imes 5}{280 imes 5} = rac{635}{1400}

Next, we compare it to rac{2}{5}:

rac{2 imes 280}{5 imes 280} = rac{560}{1400}

Since 635>560635 > 560, we conclude that the proportion of females who can speak Spanish is indeed at least rac{2}{5}.

Step 4

Conclusion

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Answer

Thus, Jeff's statement that at least 2 out of every 5 females in the town can speak Spanish is correct.

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