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Finding the Third Proportional to 7,842 and 12,006

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Solution

The third proportional to 7,842 and 12,006 is: 18,381.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,842 : 12,006 = 12,006 : x
  2. Step 2: Convert to fraction form
    7,842/12,006 = 12,006/x
  3. Step 3: Cross multiply
    7,842x = 12,006 × 12,006
  4. Step 4: Simplify right side
    7,842x = 144,144,036
  5. Step 5: Solve for x
    x = 144,144,036/7,842
  6. Step 6: Final answer
    x = 18,381.03

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.