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Finding the Third Proportional to 8,214 and 12,322

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Solution

The third proportional to 8,214 and 12,322 is: 18,484.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,214 : 12,322 = 12,322 : x
  2. Step 2: Convert to fraction form
    8,214/12,322 = 12,322/x
  3. Step 3: Cross multiply
    8,214x = 12,322 × 12,322
  4. Step 4: Simplify right side
    8,214x = 151,831,684
  5. Step 5: Solve for x
    x = 151,831,684/8,214
  6. Step 6: Final answer
    x = 18,484.50

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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.