a = first number
b = second number
c = third number
a + b + c = 20 [1]
2a + 5c = 71 [2]
4a - b = 27 [3]
Rearrange [2] and [3] to express in terms of a:
c = (71 - 2a)/5 [2]
b = 4a - 27 [3]
Sub' these into [1], rearrange and solve:
a + (4a - 27) + ((71 - 2a)/5) = 20
5a - 27 + (71 - 2a)/5 = 20
5(5a - 27) + 71 - 2a = 100
25a - 135 + 71 - 2a = 100
23a - 64 = 100
a = 164/23
Sub a-value into rearranged [2] and [3]:
c = (71 - 2(164/23))/5
= (1305/23)/5
= 261/23
b = 4(164/23) - 27
= 656/23 - 27
= 35/23
