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Finding the Third Proportional to 2,138 and 2,306

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Solution

The third proportional to 2,138 and 2,306 is: 2,487.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,138 : 2,306 = 2,306 : x
  2. Step 2: Convert to fraction form
    2,138/2,306 = 2,306/x
  3. Step 3: Cross multiply
    2,138x = 2,306 × 2,306
  4. Step 4: Simplify right side
    2,138x = 5,317,636
  5. Step 5: Solve for x
    x = 5,317,636/2,138
  6. Step 6: Final answer
    x = 2,487.20

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.