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Finding the Third Proportional to 7,821 and 16,287

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Solution

The third proportional to 7,821 and 16,287 is: 33,917.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,821 : 16,287 = 16,287 : x
  2. Step 2: Convert to fraction form
    7,821/16,287 = 16,287/x
  3. Step 3: Cross multiply
    7,821x = 16,287 × 16,287
  4. Step 4: Simplify right side
    7,821x = 265,266,369
  5. Step 5: Solve for x
    x = 265,266,369/7,821
  6. Step 6: Final answer
    x = 33,917.19

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.