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Chapter 9: Problem 126

The ingredients for making 1 dozen cupcakes are: 5 tablespoons butter 1 cup sugar 2 eggs 2 cups flour 1 cup milk If you have only 5 eggs but plenty of all of the other ingredients: (a) How many cupcakes can you make? (b) How many cups of sugar do you need to make the number of cupcakes calculated in (a)?

Short Answer

Expert verified
(a) With 5 eggs, you can make 30 cupcakes. (b) To make these 30 cupcakes, you need 2.5 cups of sugar.

Step by step solution

01

Analyze the given recipe and find the proportion for other ingredients with respect to eggs.

The given recipe includes: - 5 tablespoons butter - 1 cup sugar - 2 eggs - 2 cups flour - 1 cup milk The recipe is for 1 dozen cupcakes, which means 12 cupcakes. Now we need to find how many cupcakes can be made with 5 eggs, and how many cups of sugar are needed for that amount.
02

Calculate the proportion for the amount of eggs.

As per the given recipe, 2 eggs are needed for making 12 cupcakes. Let's find how many cupcakes we can make with 5 eggs. If 2 eggs are needed for 12 cupcakes, we can write an equation: \(x=\frac{12 \ cups}{2\ eggs}\) Now replacing the number of eggs we have, which is 5, to find the number of cupcakes: \(x=\frac{12 \ cupcakes}{2\ eggs} \times 5\ eggs\) Now, let's calculate x: \(x= 5 \times \frac{12 \ cupcakes}{2}\)
03

Solve for x and find the number of cupcakes that can be made.

Calculate x: \(x= 5 \times 6 = 30 \ cupcakes\) So, with 5 eggs, we can make 30 cupcakes.
04

Find the proportion of sugar for the cupcakes.

From the given recipe, we know that: 1 cup sugar is needed for 12 cupcakes. Now we need to find how many cups of sugar are needed for 30 cupcakes. If 1 cup of sugar is required for 12 cupcakes, we can write an equation: \(y= \frac{1\ cup\ of\ sugar}{12\ cupcakes}\) Now replacing the number of cupcakes we can make, which is 30, to find the number of cups of sugar: \(y= \frac{1\ cup\ of\ sugar}{12\ cupcakes} \times 30\ cupcakes\)
05

Solve for y and find the amount of sugar needed.

Calculate y: \(y= 30 \times \frac{1 \cup\ of\ sugar}{12}\) \(y= \frac{30\ cups\ of\ sugar}{12}\) \(y= 2.5\ cups\ of\ sugar\) So, to make 30 cupcakes, 2.5 cups of sugar are needed. #Answer#: (a) With 5 eggs, you can make 30 cupcakes. (b) To make these 30 cupcakes, you need 2.5 cups of sugar.

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