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Finding the Third Proportional to 5,214 and 9,822

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Solution

The third proportional to 5,214 and 9,822 is: 18,502.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,214 : 9,822 = 9,822 : x
  2. Step 2: Convert to fraction form
    5,214/9,822 = 9,822/x
  3. Step 3: Cross multiply
    5,214x = 9,822 × 9,822
  4. Step 4: Simplify right side
    5,214x = 96,471,684
  5. Step 5: Solve for x
    x = 96,471,684/5,214
  6. Step 6: Final answer
    x = 18,502.43

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Why These Related Problems?

These problems maintain the same ratio (1.88) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.