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Finding the Third Proportional to 83,972 and 177,424

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Solution

The third proportional to 83,972 and 177,424 is: 374,878.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,972 : 177,424 = 177,424 : x
  2. Step 2: Convert to fraction form
    83,972/177,424 = 177,424/x
  3. Step 3: Cross multiply
    83,972x = 177,424 × 177,424
  4. Step 4: Simplify right side
    83,972x = 31,479,275,776
  5. Step 5: Solve for x
    x = 31,479,275,776/83,972
  6. Step 6: Final answer
    x = 374,878.24

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.