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Finding the Third Proportional to 9,689 and 21,223

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Solution

The third proportional to 9,689 and 21,223 is: 46,487.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,689 : 21,223 = 21,223 : x
  2. Step 2: Convert to fraction form
    9,689/21,223 = 21,223/x
  3. Step 3: Cross multiply
    9,689x = 21,223 × 21,223
  4. Step 4: Simplify right side
    9,689x = 450,415,729
  5. Step 5: Solve for x
    x = 450,415,729/9,689
  6. Step 6: Final answer
    x = 46,487.33

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.