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Finding the Third Proportional to 2,105 and 2,261

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Solution

The third proportional to 2,105 and 2,261 is: 2,428.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,105 : 2,261 = 2,261 : x
  2. Step 2: Convert to fraction form
    2,105/2,261 = 2,261/x
  3. Step 3: Cross multiply
    2,105x = 2,261 × 2,261
  4. Step 4: Simplify right side
    2,105x = 5,112,121
  5. Step 5: Solve for x
    x = 5,112,121/2,105
  6. Step 6: Final answer
    x = 2,428.56

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Why These Related Problems?

These problems maintain the same ratio (1.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.