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Finding the Third Proportional to 14,209 and 21,314

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Solution

The third proportional to 14,209 and 21,314 is: 31,971.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,209 : 21,314 = 21,314 : x
  2. Step 2: Convert to fraction form
    14,209/21,314 = 21,314/x
  3. Step 3: Cross multiply
    14,209x = 21,314 × 21,314
  4. Step 4: Simplify right side
    14,209x = 454,286,596
  5. Step 5: Solve for x
    x = 454,286,596/14,209
  6. Step 6: Final answer
    x = 31,971.75

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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.