You are making cookies and are missing a key ingredient—eggs. 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 g. Assuming that an average egg weighs 34.21 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

Step 1. Determine the original ratio of butter to eggs

According to the recipe, 2 cups of butter require 3 eggs. So, the ratio of butter to eggs is: Butter : Eggs 2 : 3

02

Step 2. Find the required number of eggs for 1.33 cups of butter

Let's set up a proportion with the given ratio and the given quantity of butter (1.33 cups). \( \frac{1.33}{x} = \frac{2}{3} \)

03

Step 3. Solve for x

To solve for x, cross-multiply and then divide. x = \( \frac{(1.33)(3)}{2} \) = 1.995 We need approximately 2 eggs for 1.33 cups of butter. b. If you use all the butter (and get enough eggs), what number of cookies will you make?

04

Step 4. Set up a proportion for the number of cookies

The original recipe makes 6 dozen cookies with 2 cups of butter. We have 1.33 cups of butter, so we can set up the proportion: \( \frac{1.33}{6} = \frac{2}{x} \)

05

Step 5. Solve for x

To solve for x, cross-multiply and then divide. x = \( \frac{(1.33)(6)}{2} \) = 3.99 This means we can make approximately 4 dozen cookies with 1.33 cups of butter and 2 eggs. Assuming an average egg weighs 34.21 g: a. What quantity of butter is needed to react with all the eggs?

06

Step 6. Determine the number of eggs brought by the friend

The total weight of the eggs is 62.1 g. To find the number of eggs, we will divide the total weight by the average weight of an egg. \( \frac{62.1}{34.21} \approx 1.82 \) So, the friend brought about 1.82 eggs.

07

Step 7. Calculate the required quantity of butter for 1.82 eggs

We can use the butter-to-egg ratio from the original recipe to find the required quantity of butter for 1.82 eggs: \( \frac{x}{1.82} = \frac{2}{3} \)

08

Step 8. Solve for x

To solve for x, cross-multiply and then divide. x = \( \frac{(1.82)(2)}{3} \) = 1.21 We need 1.21 cups of butter to react with all the eggs brought by our friend. b. What number of cookies can you make?

09

Step 9. Use the given recipe's proportions to determine the number of cookies with 1.82 eggs and 1.21 cups of butter

With 1.21 cups of butter, we can determine how many dozens of cookies we can make using the recipe's proportions: \( \frac{1.21}{6} = \frac{2}{x} \)

10

Step 10. Solve for x

To solve for x, cross-multiply and then divide. x = \( \frac{(1.21)(6)}{2} \) = 3.63 So, we can make approximately 3.63 dozens of cookies with 1.82 eggs and 1.21 cups of butter. c. Which will you have left over, eggs or butter? Since we have 1.33 cups of butter and only need 1.21 cups, we will have leftover butter. d. What quantity is left over?

11

Step 11. Calculate the leftover quantity

To find out the leftover quantity of butter, subtract the required quantity from the initial quantity. Leftover butter = 1.33 - 1.21 = 0.12 So, we will have 0.12 cups of butter left over.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!