Question

A cupcake recipe makes 12 cupcakes. The recipe calls for 2 cups of granulated sugar and 2 cups of powdered sugar. How many total cups of sugar are required to make 42 cupcakes?
 A.8
B.10
C.12
D.14
E.16

Answer 1

Hint: We are simply given a question that can be solved orally but we will use a unitary method for this. We will calculate the total number of sugar cups used for 12 cupcakes and therefore no cupcakes for 1 cup sugar, then we will find 42 cupcakes.

Complete step by step solution:
Given that, A cupcake recipe makes 12 cupcakes
Then for this recipe there are two types of sugar used. 2 cups of granulated sugar and 2 cups of powdered sugar
So we are taking 4 cups of sugar in total for 12 cupcakes.
It means 1 cup of sugar for 3 cupcakes.
Now we will calculate the number of cups sugar is used for 42 cupcakes.
 \[3cupcakes \to 1cup{\text{ }}of{\text{ }}sugar\]
\[42cupcakes \to x\]
\[x = \dfrac{{42 \times 1}}{3}\]
On dividing we get,
\[x = 14\]
Thus 14 cups of sugar will be used in the recipe.
That will involve 7 cups of powdered and granulated sugar both.
So, the correct answer is “14”.

Note: Note that unitary method is generally used when we have to calculate the quantity or related to one or per thing. But we can use it to find the quantity or related unit of multiple things as we did in the problem above.
Here the amount of both sugars used is 1:1. So we can calculate their quantity separately for total cupcakes also. If their ratio varies then we have to divide the total cups in that ratio.