Question

Combined, there are 194 ​Asians, Africans,​ Europeans, and Americans in a village. The number of Asians exceeds the number of Africans and Europeans by 67. The difference between the number of Europeans and Americans is 17. If the number of Africans is​ doubled, their population exceeds the number of Europeans and Americans by 11. Determine the number of​ Asians, Africans,​ Europeans, and Americans in this village.

Answer 1

There is no solution to this problem based on the given information.

Step-by-step explanation:

To determine the number of Asians, Africans, Europeans, and Americans in the village, we can use a system of equations to represent the given information:

Let A represent the number of Asians, B represent the number of Africans, E represent the number of Europeans, and M represent the number of Americans.

From the given information:

1) A + B + E + M = 194 (equation 1)

2) A = B + E + 67 (equation 2)

3) 2B = E + M + 11 (equation 3)

We can now solve this system of equations to find the values of A, B, E, and M.

From equation 2, we can substitute B + E + 67 for A in equation 1:

(B + E + 67) + B + E + M = 194

2B + 2E + M + 67 = 194

2B + E + M = 127 (equation 4)

We can now substitute E + M + 11 for 2B in equation 3:

2B = (E + M + 11)

2B + E - E - M + 11 = 0

B + 11 = 0

B = -11

Since the number of people cannot be negative, this is not a valid solution. There may be an error in the given information.

Therefore, there is no solution to this problem based on the given information.