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Finding the Third Proportional to 205,745 and 293,649

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Solution

The third proportional to 205,745 and 293,649 is: 419,109.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,745 : 293,649 = 293,649 : x
  2. Step 2: Convert to fraction form
    205,745/293,649 = 293,649/x
  3. Step 3: Cross multiply
    205,745x = 293,649 × 293,649
  4. Step 4: Simplify right side
    205,745x = 86,229,735,201
  5. Step 5: Solve for x
    x = 86,229,735,201/205,745
  6. Step 6: Final answer
    x = 419,109.75

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.