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Finding the Third Proportional to 205 and 412

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Solution

The third proportional to 205 and 412 is: 828.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    205 : 412 = 412 : x
  2. Step 2: Convert to fraction form
    205/412 = 412/x
  3. Step 3: Cross multiply
    205x = 412 × 412
  4. Step 4: Simplify right side
    205x = 169,744
  5. Step 5: Solve for x
    x = 169,744/205
  6. Step 6: Final answer
    x = 828.02

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Why These Related Problems?

These problems maintain the same ratio (2.01) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.