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Finding the Third Proportional to 409.31 and 724.13

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Solution

The third proportional to 409.31 and 724.13 is: 1,281.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.31 : 724.13 = 724.13 : x
  2. Step 2: Convert to fraction form
    409.31/724.13 = 724.13/x
  3. Step 3: Cross multiply
    409.31x = 724.13 × 724.13
  4. Step 4: Simplify right side
    409.31x = 524,357.02
  5. Step 5: Solve for x
    x = 524,357.02/409.31
  6. Step 6: Final answer
    x = 1,281.07

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.