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Finding the Third Proportional to 12,289 and 19,223

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Solution

The third proportional to 12,289 and 19,223 is: 30,069.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,289 : 19,223 = 19,223 : x
  2. Step 2: Convert to fraction form
    12,289/19,223 = 19,223/x
  3. Step 3: Cross multiply
    12,289x = 19,223 × 19,223
  4. Step 4: Simplify right side
    12,289x = 369,523,729
  5. Step 5: Solve for x
    x = 369,523,729/12,289
  6. Step 6: Final answer
    x = 30,069.47

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.