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Finding the Third Proportional to 209 and 416

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Solution

The third proportional to 209 and 416 is: 828.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    209 : 416 = 416 : x
  2. Step 2: Convert to fraction form
    209/416 = 416/x
  3. Step 3: Cross multiply
    209x = 416 × 416
  4. Step 4: Simplify right side
    209x = 173,056
  5. Step 5: Solve for x
    x = 173,056/209
  6. Step 6: Final answer
    x = 828.02

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Why These Related Problems?

These problems maintain the same ratio (1.99) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.