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2021 WSMO Speed Round Problems/Problem 6

Revision as of 09:27, 23 December 2021 by Pinkpig (talk | contribs) (Created page with "==Problem== A bag weighs 1 pound and can hold 16 pounds of food at maximum. Danny buys 100 packages of tomatoes and 300 packages of potatoes. Tomatoes come in packages that ar...")
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Problem

A bag weighs 1 pound and can hold 16 pounds of food at maximum. Danny buys 100 packages of tomatoes and 300 packages of potatoes. Tomatoes come in packages that are $12$ ounces each and potatoes come in packages that are $24$ ounces each. If all of Danny's food must go in bags, how many pounds does Danny's total luggage weigh, including the bags? (Danny will use only as many bags as he needs).

Solution

Danny's packages weigh a total of $\frac{100\cdot12+300\cdot24}{16}=\frac{1200+7200}{16}=\frac{8400}{16}=525$ pounds. This means that we need $\left\lceil\frac{525}{16}\right\rceil=33$ bags to hold Danny's packages. Thus, the answer is $33+525=\boxed{558}$

~pinkpig

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