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Finding the Third Proportional to 97.50 and 209.63

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Solution

The third proportional to 97.50 and 209.63 is: 450.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    97.50 : 209.63 = 209.63 : x
  2. Step 2: Convert to fraction form
    97.50/209.63 = 209.63/x
  3. Step 3: Cross multiply
    97.50x = 209.63 × 209.63
  4. Step 4: Simplify right side
    97.50x = 43,942.64
  5. Step 5: Solve for x
    x = 43,942.64/97.50
  6. Step 6: Final answer
    x = 450.69

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.