SOLUTION: Once my peon went to the office of courier with 4 different envelopes. The clerk in the office measured the weights in all possible pairs. The weight obtained are 59 gms, 61 gm, 6

Question 619362: Once my peon went to the office of courier with 4 different envelopes. The clerk in the office measured the weights in all possible pairs. The weight obtained are 59 gms, 61 gm, 62 gms, 63 gms, 64 gms and 66 gms. The weight of the heaviest envelope is:?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it helps to know which pairs of envelopes were paired together to get the weights.
i will assume the following:
a + b = 59
a + c = 61
a + d = 62
b + c = 63
b + d = 64
c + d = 66
based on this analysis:
envelope d would be the heaviest at 33.5 grams.
envelope c would be the next heaviest at 32.5 grams.
envelope b would be the next heaviest at 30.5 grams.
envelope a would be the lightest at 28.5 grams.
the method of solution is to determine that:
3a + 3b + 3c + 3d = 375 grams.
you also know that:
b = 59 - a
c = 61 - a
d = 62 - a
substitute in the totals equation to solve for a.
once you solve for a, the rest follow.
your total equation becomes:
3a + 3(59-a) + 3(61-a) + 3(62-a) = 375
simplify to get:
3a + 177 - 3a + 183 - 3a + 186 - 3a = 375
combine like terms to get:
-6a + 546 = 375
subtract 545 from both sides to get:
-6a = 375 - 546 = -171
divide both sides by -6 to get:
a = 28.5
this leads to:
b = 59 - 28.5 = 30.5
c = 61 - 28.5 = 32.5
d = 62 - 28.5 = 33.5
the heaviest envelope is envelope d at 33.5 grams.

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