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Finding the Third Proportional to 6,409 and 14,080

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Solution

The third proportional to 6,409 and 14,080 is: 30,932.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,409 : 14,080 = 14,080 : x
  2. Step 2: Convert to fraction form
    6,409/14,080 = 14,080/x
  3. Step 3: Cross multiply
    6,409x = 14,080 × 14,080
  4. Step 4: Simplify right side
    6,409x = 198,246,400
  5. Step 5: Solve for x
    x = 198,246,400/6,409
  6. Step 6: Final answer
    x = 30,932.50

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.