please help i need this tonight

Question

combined there are 178 asians,Africans and Americans in a village. The number of asians exceeds the number of africans and europeans the number by 75. The difference between the number of europeans and Americans is 9. If the number of africans is doubled, their population exceeds the number of Europeans and americans by 21. determine the number of asians,africans, europeans, and americans in this village.

Answer 1

x is asians

y is americans

z is africans

E is europeans

X+y+z=178

x = (z+e)+75 -> x - z - e = 75

e-y = 9 --> -y + e = 9

2z - 21 = e+y --> 2z-y-e = 21

x + y + z = 178

x - z -e = 75

-y +e = 9

-y +2z -e = 21

eliminates e

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eq2 + eq3 --> x-y-z = 84

eq3 + eq4 --> -2y+2z = 30 --> z-y = 15

x+y+z = 178

x-y-z = 84

-y+z = 15

elimiantes z

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eq1 + eq2 --> 2x = 262 --> x = 131

eq2 + eq3 --> x-2y = 99

131 - 2y = 99

-2y = -32

y = 16

e - y = 9

e - 16 = 9

e = 25

x+y+z = 178

131 + 16 + z = 178

147 +z = 178

z = 178 - 147 = 31

131 asians

16 americans

31 africans

25 europeans