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Finding the Third Proportional to 137.64 and 206.46

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Solution

The third proportional to 137.64 and 206.46 is: 309.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    137.64 : 206.46 = 206.46 : x
  2. Step 2: Convert to fraction form
    137.64/206.46 = 206.46/x
  3. Step 3: Cross multiply
    137.64x = 206.46 × 206.46
  4. Step 4: Simplify right side
    137.64x = 42,623.70
  5. Step 5: Solve for x
    x = 42,623.70/137.64
  6. Step 6: Final answer
    x = 309.68

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.