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Finding the Fourth Proportional to 734.66, 1,102.03 and 409.78

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Solution

The fourth proportional to 734.66, 1,102.03 and 409.78 is: 614.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    734.66 : 1,102.03 = 409.78 : x
  2. Step 2: Convert to fraction form
    734.66/1,102.03 = 409.78/x
  3. Step 3: Cross multiply
    734.66x = 1,102.03 × 409.78
  4. Step 4: Simplify right side
    734.66x = 451,587.80
  5. Step 5: Solve for x
    x = 451,587.80/734.66
  6. Step 6: Final answer
    x = 614.69

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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.