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Finding the Third Proportional to 294.75 and 463.31

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Solution

The third proportional to 294.75 and 463.31 is: 728.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    294.75 : 463.31 = 463.31 : x
  2. Step 2: Convert to fraction form
    294.75/463.31 = 463.31/x
  3. Step 3: Cross multiply
    294.75x = 463.31 × 463.31
  4. Step 4: Simplify right side
    294.75x = 214,658.47
  5. Step 5: Solve for x
    x = 214,658.47/294.75
  6. Step 6: Final answer
    x = 728.27

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.