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Finding the Third Proportional to 106.50 and 206.25

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Solution

The third proportional to 106.50 and 206.25 is: 399.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.50 : 206.25 = 206.25 : x
  2. Step 2: Convert to fraction form
    106.50/206.25 = 206.25/x
  3. Step 3: Cross multiply
    106.50x = 206.25 × 206.25
  4. Step 4: Simplify right side
    106.50x = 42,539.06
  5. Step 5: Solve for x
    x = 42,539.06/106.50
  6. Step 6: Final answer
    x = 399.43

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Why These Related Problems?

These problems maintain the same ratio (1.94) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.