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Finding the Third Proportional to 177 and 343

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Solution

The third proportional to 177 and 343 is: 664.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    177 : 343 = 343 : x
  2. Step 2: Convert to fraction form
    177/343 = 343/x
  3. Step 3: Cross multiply
    177x = 343 × 343
  4. Step 4: Simplify right side
    177x = 117,649
  5. Step 5: Solve for x
    x = 117,649/177
  6. Step 6: Final answer
    x = 664.68

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Why These Related Problems?

These problems maintain the same ratio (1.94) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.