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Finding the Third Proportional to 406.13 and 578.81

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Solution

The third proportional to 406.13 and 578.81 is: 824.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    406.13 : 578.81 = 578.81 : x
  2. Step 2: Convert to fraction form
    406.13/578.81 = 578.81/x
  3. Step 3: Cross multiply
    406.13x = 578.81 × 578.81
  4. Step 4: Simplify right side
    406.13x = 335,023.91
  5. Step 5: Solve for x
    x = 335,023.91/406.13
  6. Step 6: Final answer
    x = 824.93

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.