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Finding the Third Proportional to 83 and 177.75

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Solution

The third proportional to 83 and 177.75 is: 380.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    83 : 177.75 = 177.75 : x
  2. Step 2: Convert to fraction form
    83/177.75 = 177.75/x
  3. Step 3: Cross multiply
    83x = 177.75 × 177.75
  4. Step 4: Simplify right side
    83x = 31,595.06
  5. Step 5: Solve for x
    x = 31,595.06/83
  6. Step 6: Final answer
    x = 380.66

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.