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Finding the Third Proportional to 205,724 and 313,320

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Solution

The third proportional to 205,724 and 313,320 is: 477,189.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,724 : 313,320 = 313,320 : x
  2. Step 2: Convert to fraction form
    205,724/313,320 = 313,320/x
  3. Step 3: Cross multiply
    205,724x = 313,320 × 313,320
  4. Step 4: Simplify right side
    205,724x = 98,169,422,400
  5. Step 5: Solve for x
    x = 98,169,422,400/205,724
  6. Step 6: Final answer
    x = 477,189.94

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.