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Finding the Third Proportional to 209 and 296

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Solution

The third proportional to 209 and 296 is: 419.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 296 = 296 : x
  2. Step 2: Convert to fraction form
    209/296 = 296/x
  3. Step 3: Cross multiply
    209x = 296 × 296
  4. Step 4: Simplify right side
    209x = 87,616
  5. Step 5: Solve for x
    x = 87,616/209
  6. Step 6: Final answer
    x = 419.22

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.