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Finding the Third Proportional to 106 and 113.50

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Solution

The third proportional to 106 and 113.50 is: 121.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 113.50 = 113.50 : x
  2. Step 2: Convert to fraction form
    106/113.50 = 113.50/x
  3. Step 3: Cross multiply
    106x = 113.50 × 113.50
  4. Step 4: Simplify right side
    106x = 12,882.25
  5. Step 5: Solve for x
    x = 12,882.25/106
  6. Step 6: Final answer
    x = 121.53

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Why These Related Problems?

These problems maintain the same ratio (1.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.