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Finding the Third Proportional to 289.88 and 409.69

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Solution

The third proportional to 289.88 and 409.69 is: 579.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    289.88 : 409.69 = 409.69 : x
  2. Step 2: Convert to fraction form
    289.88/409.69 = 409.69/x
  3. Step 3: Cross multiply
    289.88x = 409.69 × 409.69
  4. Step 4: Simplify right side
    289.88x = 167,843.85
  5. Step 5: Solve for x
    x = 167,843.85/289.88
  6. Step 6: Final answer
    x = 579.02

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.