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Finding the Third Proportional to 409.13 and 769.88

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Solution

The third proportional to 409.13 and 769.88 is: 1,448.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.13 : 769.88 = 769.88 : x
  2. Step 2: Convert to fraction form
    409.13/769.88 = 769.88/x
  3. Step 3: Cross multiply
    409.13x = 769.88 × 769.88
  4. Step 4: Simplify right side
    409.13x = 592,707.52
  5. Step 5: Solve for x
    x = 592,707.52/409.13
  6. Step 6: Final answer
    x = 1,448.72

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Why These Related Problems?

These problems maintain the same ratio (1.88) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.