SOLUTION: When three numbers are added two at a time, the sums are 33, 48, and 53. The sum of all three numbers is: (A) 134 (B) 86 (C) 81 (D) 67 (E) 53

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: When three numbers are added two at a time, the sums are 33, 48, and 53. The sum of all three numbers is: (A) 134 (B) 86 (C) 81 (D) 67 (E) 53      Log On

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Question 281893: When three numbers are added two at a time, the sums are 33, 48, and 53. The sum
of all three numbers is:
(A) 134 (B) 86 (C) 81 (D) 67 (E) 53

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) a%2B+b+=+33
(2) b+%2B+c+=+53
(3) a+%2B+c+=+48
This is 3 equations and 3 unknowns,
so it's solvable
Subtract (3) from (2)
(2) b+%2B+c+=+53
(3) -a+-+c+=+-48
b+-+a+=+5
Add this result to (1)
a%2B+b+=+33
-a+%2B+b+=+5
2b+=+38
b+=+19
and,
a+%2B+19+=+33
a+=+14
and,
(3) a+%2B+c+=+48
14+%2B+c+=+48
c+=+34
a+%2B+b+%2B+c+=+14+%2B+19+%2B+34
a+%2B+b+%2B+c+=+67
The answer is (D)