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Finding the Third Proportional to 409,742 and 642,765

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Solution

The third proportional to 409,742 and 642,765 is: 1,008,309.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    409,742 : 642,765 = 642,765 : x
  2. Step 2: Convert to fraction form
    409,742/642,765 = 642,765/x
  3. Step 3: Cross multiply
    409,742x = 642,765 × 642,765
  4. Step 4: Simplify right side
    409,742x = 413,146,845,225
  5. Step 5: Solve for x
    x = 413,146,845,225/409,742
  6. Step 6: Final answer
    x = 1,008,309.73

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.