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Finding the Third Proportional to 410,519 and 653,723

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Solution

The third proportional to 410,519 and 653,723 is: 1,041,008.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    410,519 : 653,723 = 653,723 : x
  2. Step 2: Convert to fraction form
    410,519/653,723 = 653,723/x
  3. Step 3: Cross multiply
    410,519x = 653,723 × 653,723
  4. Step 4: Simplify right side
    410,519x = 427,353,760,729
  5. Step 5: Solve for x
    x = 427,353,760,729/410,519
  6. Step 6: Final answer
    x = 1,041,008.48

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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.