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Finding the Third Proportional to 285,906 and 419,307

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Solution

The third proportional to 285,906 and 419,307 is: 614,951.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    285,906 : 419,307 = 419,307 : x
  2. Step 2: Convert to fraction form
    285,906/419,307 = 419,307/x
  3. Step 3: Cross multiply
    285,906x = 419,307 × 419,307
  4. Step 4: Simplify right side
    285,906x = 175,818,360,249
  5. Step 5: Solve for x
    x = 175,818,360,249/285,906
  6. Step 6: Final answer
    x = 614,951.63

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.