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Finding the Third Proportional to 199 and 421

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Solution

The third proportional to 199 and 421 is: 890.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    199 : 421 = 421 : x
  2. Step 2: Convert to fraction form
    199/421 = 421/x
  3. Step 3: Cross multiply
    199x = 421 × 421
  4. Step 4: Simplify right side
    199x = 177,241
  5. Step 5: Solve for x
    x = 177,241/199
  6. Step 6: Final answer
    x = 890.66

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.