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The population of a village is in the following ratios - OCR - GCSE Maths - Question 19 - 2017 - Paper 1
Question 19
The population of a village is in the following ratios. men : children = 11 : 3 women : children = 5 : 2 (a) Find the ratio men : women. Give your answer in its si... show full transcript
Worked Solution & Example Answer:The population of a village is in the following ratios - OCR - GCSE Maths - Question 19 - 2017 - Paper 1
Step 1
Find the ratio men : women.
Answer
To find the ratio of men to women, we first need to express both in terms of children.
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From the information given:
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For men:
Let the number of children be represented as 3x, where x is a common multiplier. Then, the number of men will be:
Therefore, number of men = 11x.
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For women, using the same variable for children:
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Let the number of children be 2y, therefore:
The number of women will be:
Therefore, number of women = 5y.
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To create a common basis for both ratios, equate the number of children:
From this, we can find a common multiplier:
Hence:
Now substituting back:
Number of men = 11(2) = 22 and Number of women = 5(3) = 15.
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Therefore, the ratio of men to women is:
Simplifying:
The final ratio is:
Therefore, men : women = 22 : 15.
Step 2
Find the total population of the village.
Answer
Given that there are 36 children in the village:
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From the earlier established ratio of children to men and women, we set a base:
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Using the ratio of children, we can find:
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Using the equation derived previously for children to total population:
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Total population = number of men + number of women + number of children
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Therefore:
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We have:
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Number of men = 22 from earlier calculations,
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Number of women = 15 from earlier calculations,
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Number of children = 36.
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Hence, total population = 22 + 15 + 36 = 73.
Thus, the total population of the village is 73.