Question 632799
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
:
 If the first is 20 points more than the second,
a = b+20
a - b = 20
:
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
:
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
:
:
To confirm this find b
86 - b = 20
b = 66
:
Total of all three scores
86 + 66 + 60 = 212





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