SOLUTION: the sum of 3 integers is 77. The sum of the first and second integers exceeds the third by 99. The third integer is 65 less than the first. Find the three integers

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Question 909336: the sum of 3 integers is 77. The sum of the first and second integers exceeds the third by 99. The third integer is 65 less than the first. Find the three integers
Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
A + B + C = 77
A + B = C + 99
C = A - 65
Substitute the known values
A + B + C = 77
(C + 99) + C = 77
2C + 99 = 77
2C = -22
C = -11
Now substitute the value of C into the 3rd equation
C = A - 65
-11 = A - 65
54 = A
Back the the first equation
A + B + C = 77
54 + B - 11 = 77
Subtract 54 and add 11 to each side
B = 34
A=54, B=34, C=-11

Check:
The sum of the first and second integers exceeds the third by 99.-- 54+34=99-11
88=88
The third integer is 65 less than the first. 54-65 = -11
the sum of 3 integers is 77. 54 + 34 - 11 = 77