SOLUTION: Kathleen is baking chocolate cupcakes. Each batch of 20 cupcakes requires {{{2/3}}} cups of cocoa. a. If Kathleen has {{{3&1/4}}} cups of cocoa, how many full batche

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Kathleen is baking chocolate cupcakes. Each batch of 20 cupcakes requires {{{2/3}}} cups of cocoa. a. If Kathleen has {{{3&1/4}}} cups of cocoa, how many full batche      Log On


   



Question 1185064: Kathleen is baking chocolate cupcakes. Each batch of 20 cupcakes requires
2%2F3 cups of cocoa.

a. If Kathleen has 3%261%2F4 cups of cocoa, how many full batches will she
be able to make?
b. If there is any cocoa left over, how much is there?

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Kathleen is baking chocolate cupcakes. Each batch of 20 cupcakes requires
2%2F3 cups of cocoa.

a. If Kathleen has 3%261%2F4 cups of cocoa, how many full batches will she
be able to make?
We determine how many handfuls of matrix%281%2C2%2C2%2F3%2Ccup%29 are contained in
matrix%281%2C2%2C3%261%2F4%2Ccup%29 by dividing matrix%281%2C2%2C3%261%2F4%2Ccup%29 by matrix%281%2C2%2C2%2F3%2Ccup%29.

3%261%2F4matrix%281%2C2%2Cdivided%2Cby%292%2F3

We invert the second and multiply:

3%261%2F4%22%22%2A%22%223%2F2

We change the first to an improper fraction:

13%2F4%22%22%2A%22%223%2F2

Multiply numerators and denominators:

39%2F8

We change that to a mixed number:

    4
 8)39
   32
    7

That's 4%267%2F9

So she can make 4 full batches.

b. If there is any cocoa left over, how much is there?
If she makes 4 batches, it will take 4%282%2F3%29=8%2F3=2%262%2F3 cups.

Left over, she will have 3%261%2F4%22%22-%22%222%262%2F3

Change both to improper fractions:

13%2F4%22%22-%22%228%2F3

Get a least common denominator of 12

39%2F12%22%22-%22%2232%2F12%22%22=%22%227%2F12 of a cup left.

Edwin