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Finding the Fourth Proportional to 683, 1,024.53 and 410.84

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Solution

The fourth proportional to 683, 1,024.53 and 410.84 is: 616.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    683 : 1,024.53 = 410.84 : x
  2. Step 2: Convert to fraction form
    683/1,024.53 = 410.84/x
  3. Step 3: Cross multiply
    683x = 1,024.53 × 410.84
  4. Step 4: Simplify right side
    683x = 420,917.91
  5. Step 5: Solve for x
    x = 420,917.91/683
  6. Step 6: Final answer
    x = 616.28

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.