Question

PLEASE HELP IF YOU CAN!!! 100 POINTS

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.

Answer 1

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

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