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Finding the Fourth Proportional to 729.76, 1,007.16 and 419.28

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Solution

The fourth proportional to 729.76, 1,007.16 and 419.28 is: 578.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.76 : 1,007.16 = 419.28 : x
  2. Step 2: Convert to fraction form
    729.76/1,007.16 = 419.28/x
  3. Step 3: Cross multiply
    729.76x = 1,007.16 × 419.28
  4. Step 4: Simplify right side
    729.76x = 422,282.04
  5. Step 5: Solve for x
    x = 422,282.04/729.76
  6. Step 6: Final answer
    x = 578.66

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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.