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Finding the Third Proportional to 7,462 and 8,182

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Solution

The third proportional to 7,462 and 8,182 is: 8,971.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,462 : 8,182 = 8,182 : x
  2. Step 2: Convert to fraction form
    7,462/8,182 = 8,182/x
  3. Step 3: Cross multiply
    7,462x = 8,182 × 8,182
  4. Step 4: Simplify right side
    7,462x = 66,945,124
  5. Step 5: Solve for x
    x = 66,945,124/7,462
  6. Step 6: Final answer
    x = 8,971.47

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.