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Finding the Fourth Proportional to 742.14, 1,024.23 and 410.61

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Solution

The fourth proportional to 742.14, 1,024.23 and 410.61 is: 566.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    742.14 : 1,024.23 = 410.61 : x
  2. Step 2: Convert to fraction form
    742.14/1,024.23 = 410.61/x
  3. Step 3: Cross multiply
    742.14x = 1,024.23 × 410.61
  4. Step 4: Simplify right side
    742.14x = 420,559.08
  5. Step 5: Solve for x
    x = 420,559.08/742.14
  6. Step 6: Final answer
    x = 566.68

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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.