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Finding the Third Proportional to 75.75 and 178.13

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Solution

The third proportional to 75.75 and 178.13 is: 418.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    75.75 : 178.13 = 178.13 : x
  2. Step 2: Convert to fraction form
    75.75/178.13 = 178.13/x
  3. Step 3: Cross multiply
    75.75x = 178.13 × 178.13
  4. Step 4: Simplify right side
    75.75x = 31,728.52
  5. Step 5: Solve for x
    x = 31,728.52/75.75
  6. Step 6: Final answer
    x = 418.86

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.