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The population of a village is in the following ratios - OCR - GCSE Maths - Question 7 - 2017 - Paper 1
Question 7
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 it... show full transcript
Worked Solution & Example Answer:The population of a village is in the following ratios - OCR - GCSE Maths - Question 7 - 2017 - Paper 1
Step 1
Find the ratio men : women.
Answer
To find the ratio of men to women, we start with the ratios given:
- Men to Children ratio: 11 : 3
- Women to Children ratio: 5 : 2
Next, we establish a common number of children in both ratios. The least common multiple of the children ratios (3 and 2) is 6. Thus, we can find equivalent ratios:
-
For men:
- If 3 children correspond to 11 men, then for 6 children, the number of men can be calculated as:
ext{Men} = rac{11}{3} imes 6 = 22
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For women:
- If 2 children correspond to 5 women, then for 6 children, the number of women can be calculated as:
ext{Women} = rac{5}{2} imes 6 = 15
Now, we can express the ratio of men to women:
yielding:
Thus, the final answer for part (a) is:
Men : Women = 22 : 15
Step 2
Find the total population of the village.
Answer
Given that there are 36 children in the village, we can use the ratios found previously to determine the total population.
From part (a), we established that:
- Ratio of children to men = 3 : 11
- Ratio of children to women = 2 : 5
We can calculate the number of men and women based on the ratio of children:
-
Men Calculation:
Since 3 children correspond to 11 men, the number of men can be calculated as follows:ext{Men} = rac{11}{3} imes 36 = 132
-
Women Calculation:
Since 2 children correspond to 5 women, the number of women can be calculated as:ext{Women} = rac{5}{2} imes 36 = 90
Now, adding the number of men, women, and children gives:
Thus, the final answer for part (b) is:
Total Population = 258