You are given 5 bales of hay. Two bales are weighed at a time, which equal the following weights:

Thanks!
Ivy

Hi Ivy,

I am assuming that these weights are in pounds. Suppose that the bales are labeled a,b,c,d,e from lightest to heaviest. The ten pairs of bales are;

ab, ac, ad, ae
bc, bd, be
cd, ce
de

Notice that each bale appears four times in the list above and thus the sum

110+112+113+114+115+116+117+118+120+121=1156

adds each bale four times. Hence the total weight of the five bales is 1156/4 = 289 pounds.
   Since a and b are the lightest bales they must together weigh 110 pounds. Since d and e are the heaviest balse they must together weigh 121 pounds. Thus bale c weighs 289 - 110 - 121 = 58 pounds.

Can you now find the weights of the other four bales?

Cheers,
Harley