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Finding the Fourth Proportional to 1,099.85, 1,649.91 and 406.34

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Solution

The fourth proportional to 1,099.85, 1,649.91 and 406.34 is: 609.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,099.85 : 1,649.91 = 406.34 : x
  2. Step 2: Convert to fraction form
    1,099.85/1,649.91 = 406.34/x
  3. Step 3: Cross multiply
    1,099.85x = 1,649.91 × 406.34
  4. Step 4: Simplify right side
    1,099.85x = 670,424.43
  5. Step 5: Solve for x
    x = 670,424.43/1,099.85
  6. Step 6: Final answer
    x = 609.56

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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.