Question

Combined, there are 198 ​Asians, Africans,​ Europeans, and Americans in a village. The number of Asians exceeds the number of Africans and Europeans by 84. The difference between the number of Europeans and Americans is 6. If the number of Africans is​ doubled, their population exceeds the number of Europeans and Americans by 26. Determine the number of​ Asians, Africans,​ Europeans, and Americans in this village.

Answer 1

Using a system of equations, the numbers in the village are given as follows:

• Asians: 134.

• Africans: 30.

• Europeans: 20.

• Americans: 14.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

• Variable x: Number of Asians.

• Variable y: Number of Africans.

• Variable z: Number of Europeans.

• Variable w: Number of Americans.

Combined, there are 198 ​Asians, Africans,​ Europeans, and Americans in a village, hence:

x + y + z + w = 198.

The number of Asians exceeds the number of Africans and Europeans by 84, hence:

x - (y + z) = 84

y + z = x - 84.

The difference between the number of Europeans and Americans is 6, hence:

z - w = 6.

If the number of Africans is​ doubled, their population exceeds the number of Europeans and Americans by 26, hence:

2y = z + w + 26.

2y - z - w = 26.

Hence the system is given by:

• x + y + z + w = 198.

• x - (y + z) = 84.

• z - w = 6.

• 2y - z - w = 26.

Using a calculator, the solution is given by:

x = 134, y = 30, z = 20, w = 14.

Hence the numbers in the village are given as follows:

• Asians: 134.

• Africans: 30.

• Europeans: 20.

• Americans: 14.

More can be learned about a system of equations at brainly.com/question/24342899

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