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Finding the Third Proportional to 7,678 and 12,031

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Solution

The third proportional to 7,678 and 12,031 is: 18,851.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,678 : 12,031 = 12,031 : x
  2. Step 2: Convert to fraction form
    7,678/12,031 = 12,031/x
  3. Step 3: Cross multiply
    7,678x = 12,031 × 12,031
  4. Step 4: Simplify right side
    7,678x = 144,744,961
  5. Step 5: Solve for x
    x = 144,744,961/7,678
  6. Step 6: Final answer
    x = 18,851.91

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.