Question

8. The population of a small village is in the following ratios:
• Adult Males: Children = 11:3
• Adult Women: Children = 5:2
The difference between the number of Adult Males and Adult Females is 28.
Find the number of children in the village.

Answer 1

Answer:

The number of children in the village is 4.67.

Step-by-step explanation:

Given the problem states that the ratio of Adult Males to Children is 11:3 and the ratio of Adult Women to Children is 5:2. We can use this information to set up two equations. Let x be the number of children in the village. Then the number of Adult Males is 11x and the number of Adult Women is 5x. The difference between the number of Adult Males and Adult Females is 28. We can then apply the equation 11x - 5x = 28, which gives us 6x = 28. by dividing both sides by 6, we get x = 28/6 = 4.67. Therefore, the number of children in the village is 4.67.

Answer 2

Answer:

24 children

Step-by-step explanation:

Given ratios:

• Adult Males: Children = 11 : 3
• Adult Females : Children = 5 : 2

Multiply the first ratio by 2 and the second ratio by 3 so that the ratios of children are the same:

• Adult Males: Children = 11 × 2 : 3 × 2 = 22 : 6
• Adult Females : Children = 5 × 3 : 2 × 3 = 15 : 6

Therefore the combined ratio is:

• Adult Males : Adult Females : Children = 22 : 15 : 6

So the ratio of Adult Males to Adult Females is 22 : 15.

If the difference between the number of Adult Males and Adult Females is 28 then:

$\implies \dfrac{22}{22+15}x-\dfrac{15}{22+15}x=28$

$\implies \dfrac{22}{37}x-\dfrac{15}{37}x=28$

$\implies \dfrac{7}{37}x=28$

$\implies 7x=1036$

$\implies x=148$

Therefore:

$\implies \textsf{Adult Males}=\dfrac{22}{37} \times 148=88$

$\implies \textsf{Adult Females}=\dfrac{15}{37} \times 148=60$

If the original ratio of Adult Males to Children is 11 : 3, and the number of Adult Males is 88:

$\implies 11:3=88:c$

$\implies \dfrac{11}{3}=\dfrac{88}{c}$

$\implies 11c=264$

$\implies c=24$

Therefore, the number of children in the village is 24.