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Finding the Fourth Proportional to 742.34, 1,024.31 and 410.78

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Solution

The fourth proportional to 742.34, 1,024.31 and 410.78 is: 566.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    742.34 : 1,024.31 = 410.78 : x
  2. Step 2: Convert to fraction form
    742.34/1,024.31 = 410.78/x
  3. Step 3: Cross multiply
    742.34x = 1,024.31 × 410.78
  4. Step 4: Simplify right side
    742.34x = 420,761.97
  5. Step 5: Solve for x
    x = 420,761.97/742.34
  6. Step 6: Final answer
    x = 566.81

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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.