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Finding the Third Proportional to 8,078 and 10,207

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Solution

The third proportional to 8,078 and 10,207 is: 12,897.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,078 : 10,207 = 10,207 : x
  2. Step 2: Convert to fraction form
    8,078/10,207 = 10,207/x
  3. Step 3: Cross multiply
    8,078x = 10,207 × 10,207
  4. Step 4: Simplify right side
    8,078x = 104,182,849
  5. Step 5: Solve for x
    x = 104,182,849/8,078
  6. Step 6: Final answer
    x = 12,897.11

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Why These Related Problems?

These problems maintain the same ratio (1.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.