Systems of equations with three variables

Question

Through 2004,the Universities of Alabama,Tennessee,and Texas have had the most appearances in college football bowl games. These three schools have had a total of 141 bowl appearances.Alabama has had 8 more appearances than Texas.Together,the number of appearances by Tennessee and Texas is 37 more than the number of appearances by Alabama.Determine the number of bowl appearances for each school.

Answer 1

Let A = Alabama appearances, T for Tennessee and X for Texas

A+T+X=141

A=T+8

T+X=37+A

Substitute to eliminate A

T+ 8 + T + X = 141 => 2T + X = 133

T + X = 37 + T + 8 => X = 45

Then 2T + 45 = 133 => T = 44

and then A = 52

Please go back and plug these answers into the original equation to be sure they are correct.