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Finding the Third Proportional to 7,678 and 16,814

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Solution

The third proportional to 7,678 and 16,814 is: 36,820.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,678 : 16,814 = 16,814 : x
  2. Step 2: Convert to fraction form
    7,678/16,814 = 16,814/x
  3. Step 3: Cross multiply
    7,678x = 16,814 × 16,814
  4. Step 4: Simplify right side
    7,678x = 282,710,596
  5. Step 5: Solve for x
    x = 282,710,596/7,678
  6. Step 6: Final answer
    x = 36,820.86

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.