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Finding the Third Proportional to 13,214 and 19,822

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Solution

The third proportional to 13,214 and 19,822 is: 29,734.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,214 : 19,822 = 19,822 : x
  2. Step 2: Convert to fraction form
    13,214/19,822 = 19,822/x
  3. Step 3: Cross multiply
    13,214x = 19,822 × 19,822
  4. Step 4: Simplify right side
    13,214x = 392,911,684
  5. Step 5: Solve for x
    x = 392,911,684/13,214
  6. Step 6: Final answer
    x = 29,734.50

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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.