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Finding the Third Proportional to 382.50 and 414.25

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Solution

The third proportional to 382.50 and 414.25 is: 448.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    382.50 : 414.25 = 414.25 : x
  2. Step 2: Convert to fraction form
    382.50/414.25 = 414.25/x
  3. Step 3: Cross multiply
    382.50x = 414.25 × 414.25
  4. Step 4: Simplify right side
    382.50x = 171,603.06
  5. Step 5: Solve for x
    x = 171,603.06/382.50
  6. Step 6: Final answer
    x = 448.64

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.