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Finding the Fourth Proportional to 463.82, 698.84 and 414.09

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Solution

The fourth proportional to 463.82, 698.84 and 414.09 is: 623.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    463.82 : 698.84 = 414.09 : x
  2. Step 2: Convert to fraction form
    463.82/698.84 = 414.09/x
  3. Step 3: Cross multiply
    463.82x = 698.84 × 414.09
  4. Step 4: Simplify right side
    463.82x = 289,380.59
  5. Step 5: Solve for x
    x = 289,380.59/463.82
  6. Step 6: Final answer
    x = 623.91

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.