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Finding the Third Proportional to 6,409 and 13,778

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Solution

The third proportional to 6,409 and 13,778 is: 29,619.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,409 : 13,778 = 13,778 : x
  2. Step 2: Convert to fraction form
    6,409/13,778 = 13,778/x
  3. Step 3: Cross multiply
    6,409x = 13,778 × 13,778
  4. Step 4: Simplify right side
    6,409x = 189,833,284
  5. Step 5: Solve for x
    x = 189,833,284/6,409
  6. Step 6: Final answer
    x = 29,619.80

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.