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Finding the Third Proportional to 180 and 382

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Solution

The third proportional to 180 and 382 is: 810.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    180 : 382 = 382 : x
  2. Step 2: Convert to fraction form
    180/382 = 382/x
  3. Step 3: Cross multiply
    180x = 382 × 382
  4. Step 4: Simplify right side
    180x = 145,924
  5. Step 5: Solve for x
    x = 145,924/180
  6. Step 6: Final answer
    x = 810.69

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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.