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Finding the Fourth Proportional to 728.78, 1,005.66 and 414

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Solution

The fourth proportional to 728.78, 1,005.66 and 414 is: 571.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    728.78 : 1,005.66 = 414 : x
  2. Step 2: Convert to fraction form
    728.78/1,005.66 = 414/x
  3. Step 3: Cross multiply
    728.78x = 1,005.66 × 414
  4. Step 4: Simplify right side
    728.78x = 416,343.24
  5. Step 5: Solve for x
    x = 416,343.24/728.78
  6. Step 6: Final answer
    x = 571.29

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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.