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Finding the Third Proportional to 21,214 and 31,198

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Solution

The third proportional to 21,214 and 31,198 is: 45,880.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    21,214 : 31,198 = 31,198 : x
  2. Step 2: Convert to fraction form
    21,214/31,198 = 31,198/x
  3. Step 3: Cross multiply
    21,214x = 31,198 × 31,198
  4. Step 4: Simplify right side
    21,214x = 973,315,204
  5. Step 5: Solve for x
    x = 973,315,204/21,214
  6. Step 6: Final answer
    x = 45,880.80

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.