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Finding the Third Proportional to 268,713 and 419,409

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Solution

The third proportional to 268,713 and 419,409 is: 654,616.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    268,713 : 419,409 = 419,409 : x
  2. Step 2: Convert to fraction form
    268,713/419,409 = 419,409/x
  3. Step 3: Cross multiply
    268,713x = 419,409 × 419,409
  4. Step 4: Simplify right side
    268,713x = 175,903,909,281
  5. Step 5: Solve for x
    x = 175,903,909,281/268,713
  6. Step 6: Final answer
    x = 654,616.30

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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.