Maria mixes 1/4 cup white sugar and 2/3 cup brown sugar to make a topping for some muffins.

Question

Maria mixes 1/4 cup white sugar and 2/3 cup brown sugar to make a topping for some muffins.  She uses 1/12 cup of the mixture to top each muffin.  Maria has 1 bag of brown and 1 bag of white sugar each containing 11 & 1/3 cups of sugar.  How many muffins can Maria top if she has a bag of each type of sugar?

Answer 1

Hi Jill,

 

I'm not certain what a "bag of each type of four" is, so I think I will not worry about it. 

 

First of all, how many muffins can Maria top with one of her mixes?  Since ? = 8/12 and ¼ = 3/12, the mix has 11/12 cups of sugar in it.  Thus, she can top eleven muffins.

 

But how many of these mixes can she make?  Since ? > ¼, Maria uses more brown sugar that white sugar for each mix.  Thus, if she has 11 ? cups of each type of sugar, she is limited by the amount of brown sugar, and she will have white sugar left over.  

 

11 ? = 33/3 + ? = 34/3.

 

Now, a good intuition would be that there are 34 thirds lying around.  Imagine them resting in 34 separate ? cup containers.  If we have to use 2 of these thirds for every mix, we can make 34/2 = 17 mixes. This intuition is completely correct.  Since each mix can top 11 muffins, Maria can top a total of

 

11*17 = 187 muffins

 

To get the answer through fraction division, you observe that

 

34/3

 2/3

 

= 34/3 * 3/2

 

= 34*3

    3*2

 

= 34/2

 

= 17

 

Finally

17 mixes * 11 muffins / mix = 187 muffins