Difference between revisions of "2021 WSMO Speed Round Problems/Problem 6"
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==Problem== | ==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 <math>12</math> ounces each and potatoes come in packages that are <math>24</math> 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). | + | 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 <math>12</math> ounces each and potatoes come in packages that are <math>24</math> ounces each. If all of Danny's food must go in bags, how many pounds does Danny's total luggage weigh, including the bags? (Note that Danny will use only as many bags as he needs and that packages have to stay together). |
==Solution 1== | ==Solution 1== | ||
Revision as of 10:56, 23 December 2021
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 
ounces each and potatoes come in packages that are 
ounces each. If all of Danny's food must go in bags, how many pounds does Danny's total luggage weigh, including the bags? (Note that Danny will use only as many bags as he needs and that packages have to stay together).
Solution 1
Since bags weigh multiples of ounces, a bag can hold at most 
ounces, meaning that Danny uses at least 
bags, or 
bags. A construction is to let the first 
bags have 
packages of potatoes and 
packages of tomatoes, while the last bag has packages of potatoes and 
package of tomatoes.
(We cannot use bags because this construction is not valid!)
