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Finding the Third Proportional to 120.75 and 194.75

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Solution

The third proportional to 120.75 and 194.75 is: 314.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    120.75 : 194.75 = 194.75 : x
  2. Step 2: Convert to fraction form
    120.75/194.75 = 194.75/x
  3. Step 3: Cross multiply
    120.75x = 194.75 × 194.75
  4. Step 4: Simplify right side
    120.75x = 37,927.56
  5. Step 5: Solve for x
    x = 37,927.56/120.75
  6. Step 6: Final answer
    x = 314.10

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.