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Finding the Third Proportional to 120,972 and 177,234

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Solution

The third proportional to 120,972 and 177,234 is: 259,662.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    120,972 : 177,234 = 177,234 : x
  2. Step 2: Convert to fraction form
    120,972/177,234 = 177,234/x
  3. Step 3: Cross multiply
    120,972x = 177,234 × 177,234
  4. Step 4: Simplify right side
    120,972x = 31,411,890,756
  5. Step 5: Solve for x
    x = 31,411,890,756/120,972
  6. Step 6: Final answer
    x = 259,662.49

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.