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Finding the Third Proportional to 259,769 and 413,711

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Solution

The third proportional to 259,769 and 413,711 is: 658,880.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    259,769 : 413,711 = 413,711 : x
  2. Step 2: Convert to fraction form
    259,769/413,711 = 413,711/x
  3. Step 3: Cross multiply
    259,769x = 413,711 × 413,711
  4. Step 4: Simplify right side
    259,769x = 171,156,791,521
  5. Step 5: Solve for x
    x = 171,156,791,521/259,769
  6. Step 6: Final answer
    x = 658,880.74

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.