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Finding the Third Proportional to 53,696 and 82,407

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Solution

The third proportional to 53,696 and 82,407 is: 126,469.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,696 : 82,407 = 82,407 : x
  2. Step 2: Convert to fraction form
    53,696/82,407 = 82,407/x
  3. Step 3: Cross multiply
    53,696x = 82,407 × 82,407
  4. Step 4: Simplify right side
    53,696x = 6,790,913,649
  5. Step 5: Solve for x
    x = 6,790,913,649/53,696
  6. Step 6: Final answer
    x = 126,469.64

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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.