The population of a village is 11000. If the number of children increases by…
2023
The population of a village is 11000. If the number of children increases by 11% and the number of adults increases by 20%, the population becomes 12660. Find the original numbers of children and adults separately.
Answer: C. 6000, 5000 — ConceptWhen a total is divided into two groups, define one variable for each group. Their original counts form one linear equation. After percentage…
- A.
7000, 4000
- B.
4500, 6500
- C.
6000, 5000
- D.
5500, 5500
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Correct answer: C
Concept
When a total is divided into two groups, define one variable for each group. Their original counts form one linear equation.
After percentage increases, multiply each original count by its growth factor. The new total forms a second linear equation, and solving the pair gives both original counts.
Application
Let C be the number of children and A be the number of adults. Then C + A = 11000.
After the increases, 1.11C + 1.20A = 12660.
Multiply the first equation by 1.11: 1.11C + 1.11A = 12210.
Subtract this equation from the new-population equation: 0.09A = 450, so A = 5000.
Substitute A = 5000 into C + A = 11000: C = 6000.
Cross-check
The original total is 6000 + 5000 = 11000.
After the increases, 6000 × 1.11 + 5000 × 1.20 = 6660 + 6000 = 12660, which reproduces the stated new population.
Result
Therefore, the village originally had 6000 children and 5000 adults.