Rebecca R. answered 08/07/18
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Experienced Elementary Math, Prealgebra, Algebra 1, and Geometry Tutor
Hi, Caitlin!
Okay, so we need to find amount of medals won.
A + B + C = 119
Country B won 8 more than Country C so:
B = C + 8
Also, Country A won 31 more than the other two combined so:
A = B + C + 31
= (C + 8) + C + 31
= 2C +39
Now we substitute into the original equation:
A + B + C = 119
(2C + 39) + (C + 8) + C = 119
4C + 47 = 119
4C = 72
C = 18
So, if B = C + 8 then B = 26
A = 2C + 39 = 75
so,
A = 75 medals
B = 26 medals
C = 18 medals