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Heavy Enough ?

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1. Bodo weighs 100 pounds more than his sister Diane. Their combined weight is 140 pounds. How many pounds does Bodo weigh?
Answer: 120

Solution:

"Bodo weighs 120 pounds" is the correct answer. His sister weighs 20 pounds. Thus, Bodo weighs 100 pounds more than his sister and their combined weight is 140 as per the problem requirements.

The common mistake is to quickly jump to the conclusion that "Bodo weighs 100 pounds and his sister weighs 40 pounds." But, Bodo would then erroneously weigh 60 pounds more than his sister.

Alternative Solution through Equations:

Let b be Bodo's weight and s be his sister's weight. Then,

bs = 100; and
b + s = 140.

On solving the above two equations, we get

b = (100 + 140) / 2 = 120.

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