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Finding the Third Proportional to 209 and 242.75

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Solution

The third proportional to 209 and 242.75 is: 281.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 242.75 = 242.75 : x
  2. Step 2: Convert to fraction form
    209/242.75 = 242.75/x
  3. Step 3: Cross multiply
    209x = 242.75 × 242.75
  4. Step 4: Simplify right side
    209x = 58,927.56
  5. Step 5: Solve for x
    x = 58,927.56/209
  6. Step 6: Final answer
    x = 281.95

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.