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Finding the Third Proportional to 180.75 and 414.88

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Solution

The third proportional to 180.75 and 414.88 is: 952.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    180.75 : 414.88 = 414.88 : x
  2. Step 2: Convert to fraction form
    180.75/414.88 = 414.88/x
  3. Step 3: Cross multiply
    180.75x = 414.88 × 414.88
  4. Step 4: Simplify right side
    180.75x = 172,121.27
  5. Step 5: Solve for x
    x = 172,121.27/180.75
  6. Step 6: Final answer
    x = 952.26

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.