Instructions
You've found an amazing cookie recipe, but it only makes a small batch. Your goal is to increase the recipe for a bake sale by calculating percentage increases and adjusting the ingredient amounts, which are listed as fractions. Read the scenario and answer the questions that follow. Show your work where required.
The Scenario
You are baking cookies for a school fundraiser. Your famous "Cosmic Chocolate Chip Cookie" recipe makes exactly 24 cookies. To have enough for the sale, you need to increase the recipe's yield by 75%. Use the original recipe below to calculate the new ingredient quantities.
Original Recipe: Cosmic Chocolate Chip Cookies
Yield: 24 cookies
- 2 ½ cups All-Purpose Flour
- 1 tsp Baking Soda
- ¾ tsp Salt
- 1 cup Butter, softened
- ¾ cup White Sugar
- 1 cup Brown Sugar
- 2 tsp Vanilla Extract
- 2 large Eggs
- 1 ¾ cups Chocolate Chips
Part 1: Scaling Up
First, let's figure out the new batch size and the multiplier you'll need.
- The original recipe makes 24 cookies. If you increase this amount by 75%, how many cookies will your new recipe make?
Work/Answer:
- To increase all ingredients by 75%, you need to multiply each one by a specific number. What is this multiplier? (Hint: You're making the original 100% PLUS an additional 75%.)
Express the multiplier as a decimal: _____________
Express the multiplier as a fraction in simplest form: _____________
Part 2: The New Ingredient List
Use the fraction multiplier from Part 1 to calculate the new amount for each ingredient. Show your calculations and write your final answer in its simplest form (use mixed numbers like 2 ½ instead of improper fractions like 5/2).
| Ingredient | Original Amount | Calculation (Original Amount × Multiplier) | New Amount |
|---|---|---|---|
| Flour | 2 ½ cups | ||
| Baking Soda | 1 tsp | ||
| Salt | ¾ tsp | ||
| White Sugar | ¾ cup | ||
| Eggs | 2 large | ||
| Chocolate Chips | 1 ¾ cups |
Part 3: Baking Brain Teasers
Solve these final challenges based on your new, larger recipe.
- The chocolate chips you buy come in a 4-cup bag. After making your new, larger batch of cookies, will you have enough chocolate chips left over to make a half-batch of the original recipe? Justify your answer with calculations.
- Oh no! You check the carton and you only have 3 eggs, not the amount required for your new recipe. If the number of eggs is your only limiting factor, what is the maximum percentage increase you can apply to the original recipe?
Answer Key
Part 1: Scaling Up
- 42 cookies.
Work: 24 × 0.75 = 18. Then, 24 + 18 = 42 cookies. -
Decimal: 1.75 (100% + 75% = 175%)
Fraction: 7/4 (175/100 simplified is 7/4)
Part 2: The New Ingredient List
| Ingredient | Original Amount | Calculation (Original Amount × Multiplier) | New Amount |
|---|---|---|---|
| Flour | 2 ½ cups | 5/2 × 7/4 = 35/8 | 4 ⅜ cups |
| Baking Soda | 1 tsp | 1 × 7/4 = 7/4 | 1 ¾ tsp |
| Salt | ¾ tsp | 3/4 × 7/4 = 21/16 | 1 ⁵/₁₆ tsp |
| White Sugar | ¾ cup | 3/4 × 7/4 = 21/16 | 1 ⁵/₁₆ cup |
| Eggs | 2 large | 2 × 7/4 = 14/4 = 7/2 | 3 ½ large |
| Chocolate Chips | 1 ¾ cups | 7/4 × 7/4 = 49/16 | 3 ¹/₁₆ cups |
Part 3: Baking Brain Teasers
- Yes, you will have enough chocolate chips left over.
Justification:- Amount used in new recipe: 3 ¹/₁₆ cups.
- Amount left in bag: 4 - 3 ¹/₁₆ = ¹⁵/₁₆ cups.
- Amount needed for half of the original recipe: 1 ¾ × ½ = 7/4 × ½ = 7/8 cups.
- Compare what's left to what's needed: Is ¹⁵/₁₆ > 7/8? To compare, find a common denominator (16). 7/8 is equal to ¹⁴/₁₆. Since ¹⁵/₁₆ is greater than ¹⁴/₁₆, you have enough.
- The maximum percentage increase is 50%.
Justification: The original recipe needs 2 eggs and you have 3. Your multiplier is limited to 3/2 (what you have / what you need). The fraction 3/2 is equal to the decimal 1.5. A multiplier of 1.5 represents the original 100% plus a 50% increase.