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Finding the Third Proportional to 289 and 419

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Solution

The third proportional to 289 and 419 is: 607.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    289 : 419 = 419 : x
  2. Step 2: Convert to fraction form
    289/419 = 419/x
  3. Step 3: Cross multiply
    289x = 419 × 419
  4. Step 4: Simplify right side
    289x = 175,561
  5. Step 5: Solve for x
    x = 175,561/289
  6. Step 6: Final answer
    x = 607.48

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.