lemon metrics problem

Problem Overview

  • Objective: Determine the cost to buy enough lemons to make four nine-inch lemon pies, each requiring three-fourths of a cup of lemon juice.

  • Known Information:

    • Price of lemons: 68¢ each

    • Each lemon yields: 4 tablespoons of juice

    • Each pie requires: $\frac{3}{4}$ cup of lemon juice

Step 1: Calculate Total Lemon Juice Needed

  • Total Number of Pies: 4 lemon pies

  • Juice Requirement per Pie: $\frac{3}{4}$ cup

  • Total Lemon Juice in Cups:

    • Calculation: Total cups = Number of pies × Juice requirement per pie

    • Total cups=4×34=3 cups\text{Total cups} = 4 \times \frac{3}{4} = 3 \text{ cups}

Step 2: Convert Cups to Tablespoons

  • Conversion Factor: 1 cup = 16 tablespoons

  • Conversion to Tablespoons:

    • Calculation:

    • To convert cups to tablespoons, use a unit fraction:

    • Total tablespoons=3 cups×16 tablespoons1 cup\text{Total tablespoons} = 3 \text{ cups} \times \frac{16 \text{ tablespoons}}{1 \text{ cup}}

    • This simplifies to:

    • 3×16=48 tablespoons3 \times 16 = 48 \text{ tablespoons}

  • Units: Total lemon juice needed is 48 tablespoons.

Step 3: Determine Number of Lemons Needed

  • Yield of Each Lemon: 4 tablespoons of lemon juice

  • Conversion from Tablespoons to Lemons:

    • Conversion factor: 1 lemon = 4 tablespoons

    • Calculation:

    • Number of lemons needed = Total tablespoons × Unit fraction for conversion

    • Number of lemons=48 tablespoons×1 lemon4 tablespoons\text{Number of lemons} = 48 \text{ tablespoons} \times \frac{1 \text{ lemon}}{4 \text{ tablespoons}}

    • This simplifies to:

    • 48÷4=12 lemons48 \div 4 = 12 \text{ lemons}

Step 4: Calculate Total Cost for Lemons

  • Cost per Lemon: 68¢

  • Total Cost Calculation:

    • Total cost = Number of lemons × Cost per lemon

    • Total cost=12 lemons×$0.68\text{Total cost} = 12 \text{ lemons} \times \$0.68

    • Calculation yields:

    • 12×0.68=8.1612 \times 0.68 = 8.16

  • Final Cost: The cost for the lemons to make four lemon pies is $8.16.

Summary

  1. Calculated the amount of lemon juice needed: 3 cups for 4 pies.

  2. Converted cups to tablespoons: 48 tablespoons of lemon juice required.

  3. Determined the number of lemons needed: 12 lemons.

  4. Found the total cost for the lemons: $8.16.

Conclusion

  • The process includes determining requirements, performing unit conversions, and calculating costs based on unit prices. The accurate steps validated the calculations for practical applications in cooking and budgeting.