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Finding the Third Proportional to 406.13 and 478.69

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Solution

The third proportional to 406.13 and 478.69 is: 564.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    406.13 : 478.69 = 478.69 : x
  2. Step 2: Convert to fraction form
    406.13/478.69 = 478.69/x
  3. Step 3: Cross multiply
    406.13x = 478.69 × 478.69
  4. Step 4: Simplify right side
    406.13x = 229,141.72
  5. Step 5: Solve for x
    x = 229,141.72/406.13
  6. Step 6: Final answer
    x = 564.21

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.