You are making cookies and are missing a key ingredienteggs. You have most of the other ingredients needed to make the cookies, except you have only \(1.33\) cups of butter and no eggs. You note that the recipe calls for two cups of butter and three eggs (plus the other ingredients) to make six dozen cookies. You call a friend and have him bring you some eggs. a. What number of eggs do you need? b. If you use all the butter (and get enough eggs), what number of cookies will you make? Unfortunately, your friend hangs up before you tell him how many eggs you need. When he arrives, he has a surprise for you-to save time, he has broken them all in a bowl for you. You ask him how many he brought, and he replies, 'I can't remember." You weigh the eggs and find that they weigh \(62.1 \mathrm{~g}\). Assuming that an average egg weighs \(34.21 \mathrm{~g}\), a. What quantity of butter is needed to react with all the eggs? b. What number of cookies can you make? c. Which will you have left over, eggs or butter? d. What quantity is left over?

Step by step solution

01

(a1) Find the number of eggs needed in the original recipe

Since the recipe calls for three eggs to make six dozen cookies, you should need 3 eggs for the original recipe.

02

(b1) Calculate the initial number of cookies you can make with the available butter

Since you have only \(1.33\) cups of butter and the original recipe calls for two cups of butter to make six dozen cookies, you can form a proportion to find out how many dozens of cookies you can make: \[ \frac{1.33}{2} = \frac{x}{6} \] Solving for x: \[ x = \frac{1.33 * 6}{2} = 3.99 \] This means you can make about 3.99 dozen cookies with the available butter.

03

(a2) Calculate the number of eggs your friend brought based on the weight

The total weight of the eggs your friend brought is 62.1 g, and the average weight of an egg is 34.21 g. To find out how many eggs your friend brought, we can divide the total weight by the average weight of an egg: \[ \text{Number of eggs} = \frac{62.1}{34.21} = 1.81 \] There are 1.81 eggs in the bowl (approximately 2 eggs).

04

(b2) Calculate the number of cookies you can make with the actual ingredients

Now that you know how many eggs your friend brought and the amount of butter you have, you can calculate how many cookies you can make with the actual ingredients. You should set up another proportion based on the original recipe: \[ \frac{2}{3} = \frac{1.33}{1.81} \] Next, you need to find the quantity of butter needed to react with all the eggs. Solving for the required butter amount: \[ \text{Butter required} = \frac{2 * 1.81}{3} = 1.2067 \] So you need 1.2067 cups of butter to react with all the eggs.

05

(c) Determine which ingredient is left over, eggs or butter

Since you have 1.33 cups of butter and only need 1.2067 cups of butter to react with all the eggs, you will have some butter left over.

06

(d) Calculate the leftover quantity

To determine the leftover quantity of butter, subtract the required amount of butter from the available amount: \[ \text{Leftover butter} = 1.33 - 1.2067 = 0.1233 \] So, you will have 0.1233 cups of butter left over.

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