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Finding the Third Proportional to 5,186 and 7,406

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Solution

The third proportional to 5,186 and 7,406 is: 10,576.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,186 : 7,406 = 7,406 : x
  2. Step 2: Convert to fraction form
    5,186/7,406 = 7,406/x
  3. Step 3: Cross multiply
    5,186x = 7,406 × 7,406
  4. Step 4: Simplify right side
    5,186x = 54,848,836
  5. Step 5: Solve for x
    x = 54,848,836/5,186
  6. Step 6: Final answer
    x = 10,576.33

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.