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Finding the Third Proportional to 6,824 and 14,337

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Solution

The third proportional to 6,824 and 14,337 is: 30,121.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,824 : 14,337 = 14,337 : x
  2. Step 2: Convert to fraction form
    6,824/14,337 = 14,337/x
  3. Step 3: Cross multiply
    6,824x = 14,337 × 14,337
  4. Step 4: Simplify right side
    6,824x = 205,549,569
  5. Step 5: Solve for x
    x = 205,549,569/6,824
  6. Step 6: Final answer
    x = 30,121.57

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.