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Finding the Third Proportional to 289 and 411

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Solution

The third proportional to 289 and 411 is: 584.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    289 : 411 = 411 : x
  2. Step 2: Convert to fraction form
    289/411 = 411/x
  3. Step 3: Cross multiply
    289x = 411 × 411
  4. Step 4: Simplify right side
    289x = 168,921
  5. Step 5: Solve for x
    x = 168,921/289
  6. Step 6: Final answer
    x = 584.50

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.