SOLUTION: The sum of a student's three scores is 210. If the first is 23 points more than the second, and the sum of the first two is 15 more than twice the third, what was the first score?

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Question 1123118: The sum of a student's three scores is 210. If the first is 23 points more than the second, and the sum of the first two is 15 more than twice the third, what was the first score?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
First           x+23
Second           x
Third            y
TOTAL           210


%28x%2B23%29%2Bx=2y%2B15


system%28%28x%2B23%29%2Bx%2By=210%2C%28x%2B23%29%2Bx=2y%2B15%29
-
system%282x%2By=187%2C2x-2y=-8%29

system%282x%2By=187%2Cx-y=-4%29
Add corresponding members.
3x=183
highlight%28x=61%29
-
highlight%2884%29,x+23

210-61-84=highlight%2865%29 
SCORE ID          VALUE
First ------------- 84
Second ----------- 61
Third ------------ 65

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of a student's three scores is 210. If the first is 23 points more than the second, and the sum of the first two is 15 more than twice the third, what was the first score?
You don''t need to find what's NOT asked. Therefore, let FIRST SCORE be F

Then 2nd score = F - 23

Also, F + F - 23 = 2T + 15, with T being the 3rd score

2F - 23 - 15 = 2T

2F - 38 = 2T

2(F - 19) = 2(T)

F - 19 = T

We then get: F + F - 23 + F - 19 = 210

3F - 42 = 210

3F = 252

F, or 1st score = highlight_green%28matrix%281%2C3%2C+252%2F3%2C+%22=%22%2C+84%29%29