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Finding the Third Proportional to 289 and 409.25

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Solution

The third proportional to 289 and 409.25 is: 579.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    289 : 409.25 = 409.25 : x
  2. Step 2: Convert to fraction form
    289/409.25 = 409.25/x
  3. Step 3: Cross multiply
    289x = 409.25 × 409.25
  4. Step 4: Simplify right side
    289x = 167,485.56
  5. Step 5: Solve for x
    x = 167,485.56/289
  6. Step 6: Final answer
    x = 579.53

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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.