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Finding the Third Proportional to 381.75 and 706.13

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Solution

The third proportional to 381.75 and 706.13 is: 1,306.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    381.75 : 706.13 = 706.13 : x
  2. Step 2: Convert to fraction form
    381.75/706.13 = 706.13/x
  3. Step 3: Cross multiply
    381.75x = 706.13 × 706.13
  4. Step 4: Simplify right side
    381.75x = 498,612.52
  5. Step 5: Solve for x
    x = 498,612.52/381.75
  6. Step 6: Final answer
    x = 1,306.12

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Why These Related Problems?

These problems maintain the same ratio (1.85) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.