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Finding the Third Proportional to 177 and 381.75

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Solution

The third proportional to 177 and 381.75 is: 823.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    177 : 381.75 = 381.75 : x
  2. Step 2: Convert to fraction form
    177/381.75 = 381.75/x
  3. Step 3: Cross multiply
    177x = 381.75 × 381.75
  4. Step 4: Simplify right side
    177x = 145,733.06
  5. Step 5: Solve for x
    x = 145,733.06/177
  6. Step 6: Final answer
    x = 823.35

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.