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Finding the Third Proportional to 269,948 and 419,070

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Solution

The third proportional to 269,948 and 419,070 is: 650,568.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    269,948 : 419,070 = 419,070 : x
  2. Step 2: Convert to fraction form
    269,948/419,070 = 419,070/x
  3. Step 3: Cross multiply
    269,948x = 419,070 × 419,070
  4. Step 4: Simplify right side
    269,948x = 175,619,664,900
  5. Step 5: Solve for x
    x = 175,619,664,900/269,948
  6. Step 6: Final answer
    x = 650,568.50

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.