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Finding the Third Proportional to 120.50 and 197.50

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Solution

The third proportional to 120.50 and 197.50 is: 323.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    120.50 : 197.50 = 197.50 : x
  2. Step 2: Convert to fraction form
    120.50/197.50 = 197.50/x
  3. Step 3: Cross multiply
    120.50x = 197.50 × 197.50
  4. Step 4: Simplify right side
    120.50x = 39,006.25
  5. Step 5: Solve for x
    x = 39,006.25/120.50
  6. Step 6: Final answer
    x = 323.70

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.