Question 632799: The sum of a student's three scores is 212. If the first is 20 points more than the second, and the sum of the first two is 32 more than twice the third, what was the first score?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Three scores, a, b, c
Write an equation for each statement:
:
The sum of a student's three scores is 212.
a + b + c = 212
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If the first is 20 points more than the second,
a = b+20
a - b = 20
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and the sum of the first two is 32 more than twice the third,
a + b = 2c + 32
a + b - 2c = 32
Subtract from the 1st equation
a + b + c = 212
a + b -2c = 32
----------------subtraction eliminates a and b
3c = 180
c = 180/3
c = 60 the 3rd score
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Find a
a + b + 60 = 212
subtract 60 from both sides
a + b = 152
Add a - b = 20 to the above equation
a + b = 152
a - b = 20
-------------addition eliminates b, find a
2a = 172
a = 172/2
a = 86 is the 1st score
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To confirm this find b
86 - b = 20
b = 66
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Total of all three scores
86 + 66 + 60 = 212
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