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Finding the Third Proportional to 6,824 and 9,744

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Solution

The third proportional to 6,824 and 9,744 is: 13,913.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,824 : 9,744 = 9,744 : x
  2. Step 2: Convert to fraction form
    6,824/9,744 = 9,744/x
  3. Step 3: Cross multiply
    6,824x = 9,744 × 9,744
  4. Step 4: Simplify right side
    6,824x = 94,945,536
  5. Step 5: Solve for x
    x = 94,945,536/6,824
  6. Step 6: Final answer
    x = 13,913.47

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.