Mikey was looking through his drawer where he was saving all of his packages of gummy fruit- candy. He found a dozen packages of candies 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 colour of each package, but not the names of the candies. Each kind of candy comes in only one colour. 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 colour 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 grey packages, and there must be 24 ÷ 12 = 2 grey 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.
