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Finding the Third Proportional to 2,357 and 2,561

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Solution

The third proportional to 2,357 and 2,561 is: 2,782.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,357 : 2,561 = 2,561 : x
  2. Step 2: Convert to fraction form
    2,357/2,561 = 2,561/x
  3. Step 3: Cross multiply
    2,357x = 2,561 × 2,561
  4. Step 4: Simplify right side
    2,357x = 6,558,721
  5. Step 5: Solve for x
    x = 6,558,721/2,357
  6. Step 6: Final answer
    x = 2,782.66

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.