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Finding the Third Proportional to 209.50 and 230.75

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Solution

The third proportional to 209.50 and 230.75 is: 254.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.50 : 230.75 = 230.75 : x
  2. Step 2: Convert to fraction form
    209.50/230.75 = 230.75/x
  3. Step 3: Cross multiply
    209.50x = 230.75 × 230.75
  4. Step 4: Simplify right side
    209.50x = 53,245.56
  5. Step 5: Solve for x
    x = 53,245.56/209.50
  6. Step 6: Final answer
    x = 254.16

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.