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Finding the Third Proportional to 12,209 and 18,314

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Solution

The third proportional to 12,209 and 18,314 is: 27,471.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,209 : 18,314 = 18,314 : x
  2. Step 2: Convert to fraction form
    12,209/18,314 = 18,314/x
  3. Step 3: Cross multiply
    12,209x = 18,314 × 18,314
  4. Step 4: Simplify right side
    12,209x = 335,402,596
  5. Step 5: Solve for x
    x = 335,402,596/12,209
  6. Step 6: Final answer
    x = 27,471.75

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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.