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Finding the Fourth Proportional to 741.78, 1,023.64 and 410.20

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Solution

The fourth proportional to 741.78, 1,023.64 and 410.20 is: 566.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    741.78 : 1,023.64 = 410.20 : x
  2. Step 2: Convert to fraction form
    741.78/1,023.64 = 410.20/x
  3. Step 3: Cross multiply
    741.78x = 1,023.64 × 410.20
  4. Step 4: Simplify right side
    741.78x = 419,893.54
  5. Step 5: Solve for x
    x = 419,893.54/741.78
  6. Step 6: Final answer
    x = 566.06

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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.