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Finding the Third Proportional to 2,406 and 5,186

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Solution

The third proportional to 2,406 and 5,186 is: 11,178.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,406 : 5,186 = 5,186 : x
  2. Step 2: Convert to fraction form
    2,406/5,186 = 5,186/x
  3. Step 3: Cross multiply
    2,406x = 5,186 × 5,186
  4. Step 4: Simplify right side
    2,406x = 26,894,596
  5. Step 5: Solve for x
    x = 26,894,596/2,406
  6. Step 6: Final answer
    x = 11,178.14

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.