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Finding the Third Proportional to 322 and 419.25

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Solution

The third proportional to 322 and 419.25 is: 545.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    322 : 419.25 = 419.25 : x
  2. Step 2: Convert to fraction form
    322/419.25 = 419.25/x
  3. Step 3: Cross multiply
    322x = 419.25 × 419.25
  4. Step 4: Simplify right side
    322x = 175,770.56
  5. Step 5: Solve for x
    x = 175,770.56/322
  6. Step 6: Final answer
    x = 545.87

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.