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Finding the Third Proportional to 12,142 and 18,214

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Solution

The third proportional to 12,142 and 18,214 is: 27,322.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,142 : 18,214 = 18,214 : x
  2. Step 2: Convert to fraction form
    12,142/18,214 = 18,214/x
  3. Step 3: Cross multiply
    12,142x = 18,214 × 18,214
  4. Step 4: Simplify right side
    12,142x = 331,749,796
  5. Step 5: Solve for x
    x = 331,749,796/12,142
  6. Step 6: Final answer
    x = 27,322.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.