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Finding the Third Proportional to 2,138 and 5,177

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Solution

The third proportional to 2,138 and 5,177 is: 12,535.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,138 : 5,177 = 5,177 : x
  2. Step 2: Convert to fraction form
    2,138/5,177 = 5,177/x
  3. Step 3: Cross multiply
    2,138x = 5,177 × 5,177
  4. Step 4: Simplify right side
    2,138x = 26,801,329
  5. Step 5: Solve for x
    x = 26,801,329/2,138
  6. Step 6: Final answer
    x = 12,535.70

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.