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Finding the Third Proportional to 178.25 and 271.50

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Solution

The third proportional to 178.25 and 271.50 is: 413.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    178.25 : 271.50 = 271.50 : x
  2. Step 2: Convert to fraction form
    178.25/271.50 = 271.50/x
  3. Step 3: Cross multiply
    178.25x = 271.50 × 271.50
  4. Step 4: Simplify right side
    178.25x = 73,712.25
  5. Step 5: Solve for x
    x = 73,712.25/178.25
  6. Step 6: Final answer
    x = 413.53

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.