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Finding the Third Proportional to 8,214 and 12,746

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Solution

The third proportional to 8,214 and 12,746 is: 19,778.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,214 : 12,746 = 12,746 : x
  2. Step 2: Convert to fraction form
    8,214/12,746 = 12,746/x
  3. Step 3: Cross multiply
    8,214x = 12,746 × 12,746
  4. Step 4: Simplify right side
    8,214x = 162,460,516
  5. Step 5: Solve for x
    x = 162,460,516/8,214
  6. Step 6: Final answer
    x = 19,778.49

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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.