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Finding the Third Proportional to 6,824 and 15,782

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Solution

The third proportional to 6,824 and 15,782 is: 36,499.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,824 : 15,782 = 15,782 : x
  2. Step 2: Convert to fraction form
    6,824/15,782 = 15,782/x
  3. Step 3: Cross multiply
    6,824x = 15,782 × 15,782
  4. Step 4: Simplify right side
    6,824x = 249,071,524
  5. Step 5: Solve for x
    x = 249,071,524/6,824
  6. Step 6: Final answer
    x = 36,499.34

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.