Question

A recipe for 114 dozen cupcakes calls for 123 cups of flour, but Rashida has only 1 cup of flour. How many cupcakes can she make? Hint: Pay close attention to the units! Enter your answer as a mixed number. For example, if your answer is 4212, enter 42 1/2

Answer 1

9 cups

Explanation:

Given

`1(1)/(4)\ dozen\ cupcakes = 1(2)/(3)\ cups`

Required

Determine the number of cupcakes for 1 flour

Represent this with x

`x = 1\ cup`

`1(1)/(4)\ dozen\ cupcakes = 1(2)/(3)\ cups`

Cross Multiply

`x * 1(2)/(3)= 1(1)/(4)\ dozen * 1`

`1(2)/(3)x = 1(1)/(4)\ dozen`

Convert fractions to improper fraction

`(5)/(3)x = (5)/(4)\ dozen`

Solve for x

`x = (5)/(4) * (3)/(5)\ dozen`

`x = (3)/(4)\ dozen`

`1\ dozen = 12`

So, we have:

`x = (3)/(4) * 12`

`x = 9\ cups`