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Finding the Third Proportional to 7,677 and 16,049

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Solution

The third proportional to 7,677 and 16,049 is: 33,550.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,677 : 16,049 = 16,049 : x
  2. Step 2: Convert to fraction form
    7,677/16,049 = 16,049/x
  3. Step 3: Cross multiply
    7,677x = 16,049 × 16,049
  4. Step 4: Simplify right side
    7,677x = 257,570,401
  5. Step 5: Solve for x
    x = 257,570,401/7,677
  6. Step 6: Final answer
    x = 33,550.92

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.