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Finding the Third Proportional to 5,214 and 8,103

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Solution

The third proportional to 5,214 and 8,103 is: 12,592.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,214 : 8,103 = 8,103 : x
  2. Step 2: Convert to fraction form
    5,214/8,103 = 8,103/x
  3. Step 3: Cross multiply
    5,214x = 8,103 × 8,103
  4. Step 4: Simplify right side
    5,214x = 65,658,609
  5. Step 5: Solve for x
    x = 65,658,609/5,214
  6. Step 6: Final answer
    x = 12,592.75

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.