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Finding the Third Proportional to 301.14 and 406.86

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Solution

The third proportional to 301.14 and 406.86 is: 549.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    301.14 : 406.86 = 406.86 : x
  2. Step 2: Convert to fraction form
    301.14/406.86 = 406.86/x
  3. Step 3: Cross multiply
    301.14x = 406.86 × 406.86
  4. Step 4: Simplify right side
    301.14x = 165,534.15
  5. Step 5: Solve for x
    x = 165,534.15/301.14
  6. Step 6: Final answer
    x = 549.69

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.