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Finding the Third Proportional to 7,677 and 12,357

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Solution

The third proportional to 7,677 and 12,357 is: 19,889.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,677 : 12,357 = 12,357 : x
  2. Step 2: Convert to fraction form
    7,677/12,357 = 12,357/x
  3. Step 3: Cross multiply
    7,677x = 12,357 × 12,357
  4. Step 4: Simplify right side
    7,677x = 152,695,449
  5. Step 5: Solve for x
    x = 152,695,449/7,677
  6. Step 6: Final answer
    x = 19,889.99

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.