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Finding the Third Proportional to 14,206 and 21,506

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Solution

The third proportional to 14,206 and 21,506 is: 32,557.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,206 : 21,506 = 21,506 : x
  2. Step 2: Convert to fraction form
    14,206/21,506 = 21,506/x
  3. Step 3: Cross multiply
    14,206x = 21,506 × 21,506
  4. Step 4: Simplify right side
    14,206x = 462,508,036
  5. Step 5: Solve for x
    x = 462,508,036/14,206
  6. Step 6: Final answer
    x = 32,557.23

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.