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Finding the Third Proportional to 209 and 317

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Solution

The third proportional to 209 and 317 is: 480.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 317 = 317 : x
  2. Step 2: Convert to fraction form
    209/317 = 317/x
  3. Step 3: Cross multiply
    209x = 317 × 317
  4. Step 4: Simplify right side
    209x = 100,489
  5. Step 5: Solve for x
    x = 100,489/209
  6. Step 6: Final answer
    x = 480.81

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.