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Finding the Fourth Proportional to 728.89, 1,005.78 and 414.20

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Solution

The fourth proportional to 728.89, 1,005.78 and 414.20 is: 571.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    728.89 : 1,005.78 = 414.20 : x
  2. Step 2: Convert to fraction form
    728.89/1,005.78 = 414.20/x
  3. Step 3: Cross multiply
    728.89x = 1,005.78 × 414.20
  4. Step 4: Simplify right side
    728.89x = 416,594.08
  5. Step 5: Solve for x
    x = 416,594.08/728.89
  6. Step 6: Final answer
    x = 571.55

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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.