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Finding the Third Proportional to 180 and 384.75

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Solution

The third proportional to 180 and 384.75 is: 822.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    180 : 384.75 = 384.75 : x
  2. Step 2: Convert to fraction form
    180/384.75 = 384.75/x
  3. Step 3: Cross multiply
    180x = 384.75 × 384.75
  4. Step 4: Simplify right side
    180x = 148,032.56
  5. Step 5: Solve for x
    x = 148,032.56/180
  6. Step 6: Final answer
    x = 822.40

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.