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Finding the Third Proportional to 9,724 and 11,182

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Solution

The third proportional to 9,724 and 11,182 is: 12,858.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,724 : 11,182 = 11,182 : x
  2. Step 2: Convert to fraction form
    9,724/11,182 = 11,182/x
  3. Step 3: Cross multiply
    9,724x = 11,182 × 11,182
  4. Step 4: Simplify right side
    9,724x = 125,037,124
  5. Step 5: Solve for x
    x = 125,037,124/9,724
  6. Step 6: Final answer
    x = 12,858.61

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.