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​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

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whitneytr12

Answer:

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! :)

   

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