Gummy Bear Combinations
Number Theory
Level
1
Gummy bears come in packs of 6 and 9. Is there a combination of these packs which gives a total of exactly 100 gummy bears?
Yes
No
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Let x and y be the number of packs of 6 and 9, respectively. Then, we want to determine whether there is a solution in positive integers to 6 x + 9 y = 1 0 0 . We can write 6 x + 9 y = 3 ( 2 x + 3 y ) , so the total number of gummy bears will always be a multiple of 3. However, 100 is not a multiple of 3, so it is impossible to get exactly 100 gummy bears.