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Finding the Third Proportional to 2,138 and 5,201

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Solution

The third proportional to 2,138 and 5,201 is: 12,652.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,138 : 5,201 = 5,201 : x
  2. Step 2: Convert to fraction form
    2,138/5,201 = 5,201/x
  3. Step 3: Cross multiply
    2,138x = 5,201 × 5,201
  4. Step 4: Simplify right side
    2,138x = 27,050,401
  5. Step 5: Solve for x
    x = 27,050,401/2,138
  6. Step 6: Final answer
    x = 12,652.20

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Why These Related Problems?

These problems maintain the same ratio (2.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.