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Finding the Third Proportional to 7,731 and 13,782

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Solution

The third proportional to 7,731 and 13,782 is: 24,569.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,731 : 13,782 = 13,782 : x
  2. Step 2: Convert to fraction form
    7,731/13,782 = 13,782/x
  3. Step 3: Cross multiply
    7,731x = 13,782 × 13,782
  4. Step 4: Simplify right side
    7,731x = 189,943,524
  5. Step 5: Solve for x
    x = 189,943,524/7,731
  6. Step 6: Final answer
    x = 24,569.08

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.