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Finding the Fourth Proportional to 742.16, 1,024.14 and 410.54

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Solution

The fourth proportional to 742.16, 1,024.14 and 410.54 is: 566.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    742.16 : 1,024.14 = 410.54 : x
  2. Step 2: Convert to fraction form
    742.16/1,024.14 = 410.54/x
  3. Step 3: Cross multiply
    742.16x = 1,024.14 × 410.54
  4. Step 4: Simplify right side
    742.16x = 420,446.85
  5. Step 5: Solve for x
    x = 420,446.85/742.16
  6. Step 6: Final answer
    x = 566.52

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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.