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Finding the Third Proportional to 3,678 and 8,178

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Solution

The third proportional to 3,678 and 8,178 is: 18,183.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,678 : 8,178 = 8,178 : x
  2. Step 2: Convert to fraction form
    3,678/8,178 = 8,178/x
  3. Step 3: Cross multiply
    3,678x = 8,178 × 8,178
  4. Step 4: Simplify right side
    3,678x = 66,879,684
  5. Step 5: Solve for x
    x = 66,879,684/3,678
  6. Step 6: Final answer
    x = 18,183.71

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.