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Finding the Third Proportional to 205,416 and 309,582

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Solution

The third proportional to 205,416 and 309,582 is: 466,570.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,416 : 309,582 = 309,582 : x
  2. Step 2: Convert to fraction form
    205,416/309,582 = 309,582/x
  3. Step 3: Cross multiply
    205,416x = 309,582 × 309,582
  4. Step 4: Simplify right side
    205,416x = 95,841,014,724
  5. Step 5: Solve for x
    x = 95,841,014,724/205,416
  6. Step 6: Final answer
    x = 466,570.35

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.