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Finding the Fourth Proportional to 729.60, 1,006.80 and 419.04

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Solution

The fourth proportional to 729.60, 1,006.80 and 419.04 is: 578.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.60 : 1,006.80 = 419.04 : x
  2. Step 2: Convert to fraction form
    729.60/1,006.80 = 419.04/x
  3. Step 3: Cross multiply
    729.60x = 1,006.80 × 419.04
  4. Step 4: Simplify right side
    729.60x = 421,889.47
  5. Step 5: Solve for x
    x = 421,889.47/729.60
  6. Step 6: Final answer
    x = 578.25

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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.