Systems of Equations Problem

Question

Combined, there are 172 Asians, Africans, Europeans, and Americans in a village. The number of Asians exceeds the number of Africans and Europeans by 57. The difference between the number of Europeans and Americans is 11. If the number of Africans is doubled, their population exceeds the number of Europeans and Americans by 37. Determine the number of Asians, Africans, Europeans, and Americans in this village.

Answer 1

Let a = # of Asians, f = # of Africans, e = # of Europeans and u = # of 'Americans'. Then the other statements translate into these equations:

 

a+f+e+u = 172.

 

a = f+e+57

 

e - u = 11

 

This is a system of four linear equations in four variables, and you may solve it by numerous means that are covered in Algebra II or College Algebra courses.

 

Check the equations (including my typing) & make sure that the solutions are all non-negative integers.

 

2f = e+ u +37