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Finding the Third Proportional to 209 and 243

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Solution

The third proportional to 209 and 243 is: 282.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 243 = 243 : x
  2. Step 2: Convert to fraction form
    209/243 = 243/x
  3. Step 3: Cross multiply
    209x = 243 × 243
  4. Step 4: Simplify right side
    209x = 59,049
  5. Step 5: Solve for x
    x = 59,049/209
  6. Step 6: Final answer
    x = 282.53

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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.