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Finding the Fourth Proportional to 1,102, 1,648.92 and 684.16

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Solution

The fourth proportional to 1,102, 1,648.92 and 684.16 is: 1,023.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,102 : 1,648.92 = 684.16 : x
  2. Step 2: Convert to fraction form
    1,102/1,648.92 = 684.16/x
  3. Step 3: Cross multiply
    1,102x = 1,648.92 × 684.16
  4. Step 4: Simplify right side
    1,102x = 1,128,125.11
  5. Step 5: Solve for x
    x = 1,128,125.11/1,102
  6. Step 6: Final answer
    x = 1,023.71

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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.