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Finding the Third Proportional to 291,431 and 463,403

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Solution

The third proportional to 291,431 and 463,403 is: 736,854.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    291,431 : 463,403 = 463,403 : x
  2. Step 2: Convert to fraction form
    291,431/463,403 = 463,403/x
  3. Step 3: Cross multiply
    291,431x = 463,403 × 463,403
  4. Step 4: Simplify right side
    291,431x = 214,742,340,409
  5. Step 5: Solve for x
    x = 214,742,340,409/291,431
  6. Step 6: Final answer
    x = 736,854.83

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.