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Lesson 1-5: Proportional Problem Solving

Scenario: Baking Recipe Scaling - Scale recipes and calculate costs!

Duration: 60-75 minutesScenario: Baking Recipe Scaling

Learning Objectives

  • Solve multi-step proportional problems
  • Scale recipes and calculate ingredient amounts
  • Calculate costs and make budget decisions
  • Verify solutions using different methods

Recipe Scaling Problem

Original Recipe

A cookie recipe makes 12 cookies and requires 2 cups of flour. You want to make 30 cookies. If flour costs $1.20 per cup, how much will the flour cost for the larger batch?

Problem Breakdown:

  • • Find how much flour is needed for 30 cookies
  • • Calculate the cost of that flour

Step-by-Step Solution

Step 1: Set up the proportion

Original: 12 cookies need 2 cups flour
New: 30 cookies need x cups flour
Proportion: 12/2 = 30/x

Step 2: Solve for x

12/2 = 30/x
6 = 30/x
x = 30/6 = 5 cups

Step 3: Calculate cost

Cost = 5 cups × $1.20/cup = $6.00

Answer: You need 5 cups of flour, which will cost $6.00.

Alternative Method: Unit Rate

Using Unit Rate Approach

Step 1: Find flour per cookie

2 cups ÷ 12 cookies = 1/6 cup per cookie

Step 2: Calculate flour for 30 cookies

30 cookies × (1/6 cup per cookie) = 5 cups

Step 3: Calculate cost

5 cups × $1.20/cup = $6.00

Extension Problem

Limited Ingredients

If you only have 3 cups of flour available, what's the maximum number of cookies you can make?

Method 1: Using unit rate

3 cups ÷ (1/6 cup per cookie) = 3 × 6 = 18 cookies

Method 2: Using proportion

12/2 = x/3
6 = x/3
x = 18 cookies

Answer: With 3 cups of flour, you can make a maximum of 18 cookies.

Practice Problems

Problem 1

A cake recipe serves 8 people and uses 3 eggs. If you want to serve 20 people, how many eggs do you need?

Your solution:

Problem 2

A paint mixture uses 4 parts blue to 1 part white. If you have 2 cups of white paint, how much blue paint do you need?

Your solution: