combined, there are 180 asians, africans, europeans, and americans in a village. the number of asians exceeds the number of africans and europeans by 71. the difference between the number of europeans and americans is 8. if the number of africans is doubled, their population exceeds the number of europeans and americans by 20. determine the number of asians, africans, europeans, and americans in this village

r = 119, x = 27, y = 21, z = 13

Step-by-step explanation:

Let's define the variables:

r is Asians

x is Africans

y is Europeans

z is Americans

Now, we need to put the information into a equations.

r+x+y+z =  180 (1)

r = x+y+71 (2)

y-z = 8 (3)

2x = y+z+20 (4)

Let's put (2) in (1) and simplify the equation:

2x+2y+z = 109 (5)

Solve (4) for z and replace it in (5)  

z = 2x-y-20

4x+y = 129 (6)

We can solve (3) for z and replace this in (4).

z = y-8

2x = 2y+12 (7)

No we can find x and y combining  (6) and (7)

4y + 24 + y = 129

5y = 105

y = 21

Then using 3 we have:

z = 13

With (4) we can find x:

x = (21+13+20)/2 = 27

x = 27

Finally r will be:

r = 27+21+71 = 119

r = 119

Have a nice day! :)