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Finding the Third Proportional to 180.50 and 382.25

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Solution

The third proportional to 180.50 and 382.25 is: 809.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    180.50 : 382.25 = 382.25 : x
  2. Step 2: Convert to fraction form
    180.50/382.25 = 382.25/x
  3. Step 3: Cross multiply
    180.50x = 382.25 × 382.25
  4. Step 4: Simplify right side
    180.50x = 146,115.06
  5. Step 5: Solve for x
    x = 146,115.06/180.50
  6. Step 6: Final answer
    x = 809.50

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.