Today From Bedtime Math: The Best Cupcake Combo

3 flavors of icing, 2 kinds of cake…what&s the best cupcake you can make? A tasty challenge from Bedtime Math.
By Laura Overdeck
May 05, 2015

Ages

3-13


May 05, 2015

Do you know what a number cake is? Guess what — you've probably eaten one! That's what cupcakes were first called when they were first made in the 1800s. That's because the first recipes called for 1 cup of butter, 2 cups of sugar, 3 cups of flour, 4 eggs, 1 cup of milk…okay, and 1 spoonful of baking soda. We now make them by mixing in other flavors, and even more important is the frosting. We love this set of cupcakes shown here because it matches each type of frosting (chocolate, coffee, and vanilla) with each cake flavor (chocolate and yellow). Of course, people like some frosting flavors more than others…so you have to do the math to see if all cupcake fans will get their favorite.

See if you and your kids can come up with the answers to these cupcake-inspired math questions:

Wee ones: How many colors of frosting can you count?

Little kids: How many cupcakes can you count?  Bonus: If 4 of them have coffee frosting, how many don't?

Big kids: If you instead had 3 kinds of cupcake cake – chocolate, yellow, and red velvet – with 5 kinds of frosting – chocolate, vanilla, coffee, cream cheese, and pink – how many combinations of 1 cake flavor and 1 frosting flavor could you come up with?  Bonus: If you have 5 cake flavors and you want to make at least 32 different cake/icing pairs, how many icing flavors do you need to make?

The sky's the limit: If the number of cake flavors and icing flavors add up to 10, and together they can make 24 kinds of cake/icing pairs, how many cake and icing flavors could there be?
 
Answers:
Wee ones: 3 in total.

Little kids: 12 cupcakes.  Bonus: 8 cupcakes.

Big kids: 15 combinations: 5 icings for each cake flavor.  Bonus: You'll need 7 flavors, since 6 flavors would give you only 30 pairs.

The sky's the limit: There are either 4 cake flavors topped with 6 types of icing, or 6 cake flavors and 4 types of icing. If there are 24 pairs possible, you need 2 numbers that multiply to 24 that also add up to 10. The factor pairs that multiply to 24 are 1 and 24, 2 and 12, 3 and 8, and 4 and 6. 4 and 6 is the only one that adds up to 10, so they are the number of cake and icing flavors, or the other way around.

 

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