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Finding the Third Proportional to 10,214 and 15,322

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Solution

The third proportional to 10,214 and 15,322 is: 22,984.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,214 : 15,322 = 15,322 : x
  2. Step 2: Convert to fraction form
    10,214/15,322 = 15,322/x
  3. Step 3: Cross multiply
    10,214x = 15,322 × 15,322
  4. Step 4: Simplify right side
    10,214x = 234,763,684
  5. Step 5: Solve for x
    x = 234,763,684/10,214
  6. Step 6: Final answer
    x = 22,984.50

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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.