Question

Brandy places weights measuring 1 gram, 5 grams, and 10 grams on the right side of a pan balance. She has a box of 2-gram weights and a box of 4-gram weights. Which combination of weights cannot be placed on the left side if Brandy wants the pans to balance?

Answer 1

Brandy cannot balance 16 grams with an odd combination of 2-gram weights using 2-gram and 4-gram weights, because that combination would result in an odd total weight.

Step-by-step explanation:

Brandy has placed weights of 1 gram, 5 grams, and 10 grams on the right side of a double-pan mechanical balance, totaling 16 grams. With access to only 2-gram and 4-gram weights for the left side, she must find a combination that equals 16 grams.

Combinations of two 2-gram weights and two 4-gram weights (2+2+4+4) or one 2-gram weight and three 4-gram weights (2+4+4+4) would both total 12 grams, which would be insufficient.

However, one combination that cannot possibly balance the scales, given the weights available, is any combination that includes an odd number of 2-gram weights without compensating with additional weight, since the total will always be an odd number, which cannot equal the even 16 grams on the other side.