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Finding the Third Proportional to 120 and 178.25

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Solution

The third proportional to 120 and 178.25 is: 264.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    120 : 178.25 = 178.25 : x
  2. Step 2: Convert to fraction form
    120/178.25 = 178.25/x
  3. Step 3: Cross multiply
    120x = 178.25 × 178.25
  4. Step 4: Simplify right side
    120x = 31,773.06
  5. Step 5: Solve for x
    x = 31,773.06/120
  6. Step 6: Final answer
    x = 264.78

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.