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Finding the Third Proportional to 198 and 242.25

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Solution

The third proportional to 198 and 242.25 is: 296.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    198 : 242.25 = 242.25 : x
  2. Step 2: Convert to fraction form
    198/242.25 = 242.25/x
  3. Step 3: Cross multiply
    198x = 242.25 × 242.25
  4. Step 4: Simplify right side
    198x = 58,685.06
  5. Step 5: Solve for x
    x = 58,685.06/198
  6. Step 6: Final answer
    x = 296.39

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.