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Finding the Fourth Proportional to 1,099.84, 1,649.67 and 406.48

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Solution

The fourth proportional to 1,099.84, 1,649.67 and 406.48 is: 609.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,099.84 : 1,649.67 = 406.48 : x
  2. Step 2: Convert to fraction form
    1,099.84/1,649.67 = 406.48/x
  3. Step 3: Cross multiply
    1,099.84x = 1,649.67 × 406.48
  4. Step 4: Simplify right side
    1,099.84x = 670,557.86
  5. Step 5: Solve for x
    x = 670,557.86/1,099.84
  6. Step 6: Final answer
    x = 609.69

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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.