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Finding the Fourth Proportional to 419.47, 577.19 and 406.80

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Solution

The fourth proportional to 419.47, 577.19 and 406.80 is: 559.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    419.47 : 577.19 = 406.80 : x
  2. Step 2: Convert to fraction form
    419.47/577.19 = 406.80/x
  3. Step 3: Cross multiply
    419.47x = 577.19 × 406.80
  4. Step 4: Simplify right side
    419.47x = 234,801.91
  5. Step 5: Solve for x
    x = 234,801.91/419.47
  6. Step 6: Final answer
    x = 559.76

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.