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Finding the Third Proportional to 208.50 and 231.75

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Solution

The third proportional to 208.50 and 231.75 is: 257.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    208.50 : 231.75 = 231.75 : x
  2. Step 2: Convert to fraction form
    208.50/231.75 = 231.75/x
  3. Step 3: Cross multiply
    208.50x = 231.75 × 231.75
  4. Step 4: Simplify right side
    208.50x = 53,708.06
  5. Step 5: Solve for x
    x = 53,708.06/208.50
  6. Step 6: Final answer
    x = 257.59

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.