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Finding the Fourth Proportional to 742.32, 1,024.41 and 410.74

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Solution

The fourth proportional to 742.32, 1,024.41 and 410.74 is: 566.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    742.32 : 1,024.41 = 410.74 : x
  2. Step 2: Convert to fraction form
    742.32/1,024.41 = 410.74/x
  3. Step 3: Cross multiply
    742.32x = 1,024.41 × 410.74
  4. Step 4: Simplify right side
    742.32x = 420,766.16
  5. Step 5: Solve for x
    x = 420,766.16/742.32
  6. Step 6: Final answer
    x = 566.83

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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.