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Finding the Third Proportional to 19,822 and 21,685

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Solution

The third proportional to 19,822 and 21,685 is: 23,723.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,822 : 21,685 = 21,685 : x
  2. Step 2: Convert to fraction form
    19,822/21,685 = 21,685/x
  3. Step 3: Cross multiply
    19,822x = 21,685 × 21,685
  4. Step 4: Simplify right side
    19,822x = 470,239,225
  5. Step 5: Solve for x
    x = 470,239,225/19,822
  6. Step 6: Final answer
    x = 23,723.10

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.