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Finding the Fourth Proportional to 596.40, 823.42 and 409.83

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Solution

The fourth proportional to 596.40, 823.42 and 409.83 is: 565.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    596.40 : 823.42 = 409.83 : x
  2. Step 2: Convert to fraction form
    596.40/823.42 = 409.83/x
  3. Step 3: Cross multiply
    596.40x = 823.42 × 409.83
  4. Step 4: Simplify right side
    596.40x = 337,462.22
  5. Step 5: Solve for x
    x = 337,462.22/596.40
  6. Step 6: Final answer
    x = 565.83

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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.