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Finding the Third Proportional to 412,419 and 619,719

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Solution

The third proportional to 412,419 and 619,719 is: 931,217.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    412,419 : 619,719 = 619,719 : x
  2. Step 2: Convert to fraction form
    412,419/619,719 = 619,719/x
  3. Step 3: Cross multiply
    412,419x = 619,719 × 619,719
  4. Step 4: Simplify right side
    412,419x = 384,051,638,961
  5. Step 5: Solve for x
    x = 384,051,638,961/412,419
  6. Step 6: Final answer
    x = 931,217.13

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.