### Brain Teasers

# Yummie Gummies

Mikey was looking through his drawer where he was saving all of his packages of gummy fruit candy. He found a dozen packages of candy altogether. He kept a chart listing how many pieces of candy there were in each package and figured out that he had 81 pieces of candy in all. His chart listed the color of each package, but not the names of the candy. Each kind of candy comes in only one color. The chart looked like this:

Green packages 2 pieces per package

Yellow packages 5 pieces per package

Brown packages 9 pieces per package

Gray packages 12 pieces per package

Each Zing Zong is so big that these packages contain the fewest candies. There are an equal number of Zing Zong packages as Gummy Ape packages. There are 2 dozen pieces of Egg Smasher candies, and a dozen more pieces of Power Busters than Egg Smashers.

Which candy is in each color package, and how many packages of each kind does Mikey have?

Green packages 2 pieces per package

Yellow packages 5 pieces per package

Brown packages 9 pieces per package

Gray packages 12 pieces per package

Each Zing Zong is so big that these packages contain the fewest candies. There are an equal number of Zing Zong packages as Gummy Ape packages. There are 2 dozen pieces of Egg Smasher candies, and a dozen more pieces of Power Busters than Egg Smashers.

Which candy is in each color package, and how many packages of each kind does Mikey have?

### Answer

Looking at the column that shows the number of pieces per package, you can see that 12 is the only number left in this column that is a factor of 24, so Egg Smashers belong in the gray packages, and there must be 24 ÷ 12 = 2 gray packages.Looking at the same column, you can see that 9 is a factor of 36 but 5 is not, so Power Busters come in the brown packages, and there must be 36 ÷ 9 = 4 brown packages.

You now know that Gummy Apes come in the yellow packages. You also know that there are 12 - 4 - 2 = 6 packages to be accounted for, of which 3 are green and 3 are yellow. So, there must be a total of 3 x 2 = 6 pieces of Zing Zong and 3 x 5 = 15 Gummy Ape candies.

Check the total pieces of candy: 24 + 36 + 6 + 15 = 81.

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