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Finding the Third Proportional to 269,784 and 419,580

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Solution

The third proportional to 269,784 and 419,580 is: 652,549.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    269,784 : 419,580 = 419,580 : x
  2. Step 2: Convert to fraction form
    269,784/419,580 = 419,580/x
  3. Step 3: Cross multiply
    269,784x = 419,580 × 419,580
  4. Step 4: Simplify right side
    269,784x = 176,047,376,400
  5. Step 5: Solve for x
    x = 176,047,376,400/269,784
  6. Step 6: Final answer
    x = 652,549.36

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.