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Finding the Fourth Proportional to 1,099.73, 1,649.42 and 406.73

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Solution

The fourth proportional to 1,099.73, 1,649.42 and 406.73 is: 610.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,099.73 : 1,649.42 = 406.73 : x
  2. Step 2: Convert to fraction form
    1,099.73/1,649.42 = 406.73/x
  3. Step 3: Cross multiply
    1,099.73x = 1,649.42 × 406.73
  4. Step 4: Simplify right side
    1,099.73x = 670,860.38
  5. Step 5: Solve for x
    x = 670,860.38/1,099.73
  6. Step 6: Final answer
    x = 610.02

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.