SOLUTION: the sum of a students three scores is 220. if the first is 23 points more than the second, and the sum of the first two is 31 more than twice the third what was the first score

Question 1033621: the sum of a students three scores is 220. if the first is 23 points more than the second, and the sum of the first two is 31 more than twice the third what was the first score
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
A couple of ways to solve this...but let's call the three test scores, x, y and z. Then we can write
x + y + z = 220
x = y + 23
x + y = 31 + 2z
Let us then substitute the third one into the first one and get
31+2z + z = 220
3z + 31 = 220
3z = 189
z = 63
Now substitute the second equation into the first, including 63 for z...
y+23 + y + 63 = 220
2y + 86 = 220
2y = 134
y = 67
and since x = y + 23,
x = 90
Thus the scores were 90, 67, and 63.
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