- 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 isdoubled, 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