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Finding the Third Proportional to 205 and 410

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Solution

The third proportional to 205 and 410 is: 820

Step by Step Solution

  1. Step 1: Write the proportion equation
    205 : 410 = 410 : x
  2. Step 2: Convert to fraction form
    205/410 = 410/x
  3. Step 3: Cross multiply
    205x = 410 × 410
  4. Step 4: Simplify right side
    205x = 168,100
  5. Step 5: Solve for x
    x = 168,100/205
  6. Step 6: Final answer
    x = 820

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Why These Related Problems?

These problems maintain the same ratio (2) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.