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Finding the Third Proportional to 14,080 and 31,744

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Solution

The third proportional to 14,080 and 31,744 is: 71,568.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,080 : 31,744 = 31,744 : x
  2. Step 2: Convert to fraction form
    14,080/31,744 = 31,744/x
  3. Step 3: Cross multiply
    14,080x = 31,744 × 31,744
  4. Step 4: Simplify right side
    14,080x = 1,007,681,536
  5. Step 5: Solve for x
    x = 1,007,681,536/14,080
  6. Step 6: Final answer
    x = 71,568.29

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Why These Related Problems?

These problems maintain the same ratio (2.25) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.