Question 1123470: if three positive integers are added two at a time, the sums are 998, 1050, and 1234. the difference between the largest and the smallest number is:
A) 224
B) 236
C) 248
D) 250
E) 262
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52896)   (Show Source):
You can put this solution on YOUR website! .
Then the difference between the largest and smallest is 1234 - 998 = 236.
Solution
998 = the sum of the smallest and the middle numbers;
1234 = the sum of the middle and the greatest number.
When you take the difference, the middle terms will cancel each other, and you will get what the question is asking for.
Solved.
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The lesson to learn from this solution is THIS :
You do not need to find each number individually to get the answer.
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website!
let’s three positive integers be  , , and 
if added two at a time, we have sums as
 ,  , and 
if the sums are  ,  , and  , we have
 ........eq.1
 ........eq.2
 ........eq.3
--------------------------------------------solve this system
........eq.1....solve for
 ........eq.a
........eq.2....solve for
 .........eq.b
from eq.a and eq.b we have:
 ....solve for
 .................eq.c
substitute in ........eq.3
now find
.................eq.c
and, find
........eq.a
so your numbers are:
 ->the largest
 ->the smallest
and, the difference between the largest and the smallest number is:
so, your answer is: B) 
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