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Finding the Fourth Proportional to 742.09, 1,023.97 and 410.53

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Solution

The fourth proportional to 742.09, 1,023.97 and 410.53 is: 566.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    742.09 : 1,023.97 = 410.53 : x
  2. Step 2: Convert to fraction form
    742.09/1,023.97 = 410.53/x
  3. Step 3: Cross multiply
    742.09x = 1,023.97 × 410.53
  4. Step 4: Simplify right side
    742.09x = 420,363.23
  5. Step 5: Solve for x
    x = 420,363.23/742.09
  6. Step 6: Final answer
    x = 566.46

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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.