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Finding the Third Proportional to 5,214 and 12,309

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Solution

The third proportional to 5,214 and 12,309 is: 29,058.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,214 : 12,309 = 12,309 : x
  2. Step 2: Convert to fraction form
    5,214/12,309 = 12,309/x
  3. Step 3: Cross multiply
    5,214x = 12,309 × 12,309
  4. Step 4: Simplify right side
    5,214x = 151,511,481
  5. Step 5: Solve for x
    x = 151,511,481/5,214
  6. Step 6: Final answer
    x = 29,058.59

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.