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Combined, there are 182 ​Asians, Africans,​ Europeans, and Americans in a village. The number of Asians exceeds the number of Africans and Europeans by 59. The difference between the number of Europeans and Americans is 14. If the number of Africans is​doubled, their population exceeds the number of Europeans and Americans by 16. Determine the number of​ Asians, Africans,​Europeans, and Americans in this village.

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- Asians - 114, Africans - 28,​ Europeans - 27, Americans - 13

Step-by-step explanation:

Let

- Asians - a,
- Africans - b,​
- Europeans - c,
- Americans - d

Eqautions as per question

Combined, there are 182 ​Asians, Africans,​ Europeans, and Americans in a village.

- a + b + c + d = 182

The number of Asians exceeds the number of Africans and Europeans by 59.

- a = b + c + 59

The difference between the number of Europeans and Americans is 14.

- c - d = 14 ⇒ c = d + 14

If the number of Africans is​doubled, their population exceeds the number of Europeans and Americans by 16

- 2b = c + d + 16 ⇒ 2b = d + 14 + d + 16 ⇒ 2b = 2d + 30 ⇒ b = d + 15

Substitute a, b and c into the first equation and solve for d

- (b + c + 59) + b + c + d = 182
- d + 15 + d + 14 + 59 + d + 15 + d + 14 + d = 182
- 5d + 117 = 182
- 5d = 182 - 117
- 5d = 65
- d = 65/5
- d = 13

Find the other variables

- b = 13 + 15 = 28
- c = 13 + 14 = 27
- a = 28 + 27 + 59 = 114

We found that

- Asians - 114, Africans - 28,​ Europeans - 27, Americans - 13
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