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Finding the Third Proportional to 102.25 and 122.50

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Solution

The third proportional to 102.25 and 122.50 is: 146.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    102.25 : 122.50 = 122.50 : x
  2. Step 2: Convert to fraction form
    102.25/122.50 = 122.50/x
  3. Step 3: Cross multiply
    102.25x = 122.50 × 122.50
  4. Step 4: Simplify right side
    102.25x = 15,006.25
  5. Step 5: Solve for x
    x = 15,006.25/102.25
  6. Step 6: Final answer
    x = 146.76

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.