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Finding the Fourth Proportional to 507.42, 698.22 and 413.82

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Solution

The fourth proportional to 507.42, 698.22 and 413.82 is: 569.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    507.42 : 698.22 = 413.82 : x
  2. Step 2: Convert to fraction form
    507.42/698.22 = 413.82/x
  3. Step 3: Cross multiply
    507.42x = 698.22 × 413.82
  4. Step 4: Simplify right side
    507.42x = 288,937.40
  5. Step 5: Solve for x
    x = 288,937.40/507.42
  6. Step 6: Final answer
    x = 569.42

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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.