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Finding the Third Proportional to 33,407 and 77,685

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Solution

The third proportional to 33,407 and 77,685 is: 180,649.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    33,407 : 77,685 = 77,685 : x
  2. Step 2: Convert to fraction form
    33,407/77,685 = 77,685/x
  3. Step 3: Cross multiply
    33,407x = 77,685 × 77,685
  4. Step 4: Simplify right side
    33,407x = 6,034,959,225
  5. Step 5: Solve for x
    x = 6,034,959,225/33,407
  6. Step 6: Final answer
    x = 180,649.54

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.