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Finding the Third Proportional to 7,782 and 16,858

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Solution

The third proportional to 7,782 and 16,858 is: 36,519.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,782 : 16,858 = 16,858 : x
  2. Step 2: Convert to fraction form
    7,782/16,858 = 16,858/x
  3. Step 3: Cross multiply
    7,782x = 16,858 × 16,858
  4. Step 4: Simplify right side
    7,782x = 284,192,164
  5. Step 5: Solve for x
    x = 284,192,164/7,782
  6. Step 6: Final answer
    x = 36,519.17

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.