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Finding the Third Proportional to 7,686 and 16,074

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Solution

The third proportional to 7,686 and 16,074 is: 33,616.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,686 : 16,074 = 16,074 : x
  2. Step 2: Convert to fraction form
    7,686/16,074 = 16,074/x
  3. Step 3: Cross multiply
    7,686x = 16,074 × 16,074
  4. Step 4: Simplify right side
    7,686x = 258,373,476
  5. Step 5: Solve for x
    x = 258,373,476/7,686
  6. Step 6: Final answer
    x = 33,616.12

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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.