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Finding the Third Proportional to 97 and 209.50

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Solution

The third proportional to 97 and 209.50 is: 452.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    97 : 209.50 = 209.50 : x
  2. Step 2: Convert to fraction form
    97/209.50 = 209.50/x
  3. Step 3: Cross multiply
    97x = 209.50 × 209.50
  4. Step 4: Simplify right side
    97x = 43,890.25
  5. Step 5: Solve for x
    x = 43,890.25/97
  6. Step 6: Final answer
    x = 452.48

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.