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Finding the Third Proportional to 12,706 and 19,778

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Solution

The third proportional to 12,706 and 19,778 is: 30,786.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,706 : 19,778 = 19,778 : x
  2. Step 2: Convert to fraction form
    12,706/19,778 = 19,778/x
  3. Step 3: Cross multiply
    12,706x = 19,778 × 19,778
  4. Step 4: Simplify right side
    12,706x = 391,169,284
  5. Step 5: Solve for x
    x = 391,169,284/12,706
  6. Step 6: Final answer
    x = 30,786.19

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.