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Finding the Third Proportional to 96 and 165.75

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Solution

The third proportional to 96 and 165.75 is: 286.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    96 : 165.75 = 165.75 : x
  2. Step 2: Convert to fraction form
    96/165.75 = 165.75/x
  3. Step 3: Cross multiply
    96x = 165.75 × 165.75
  4. Step 4: Simplify right side
    96x = 27,473.06
  5. Step 5: Solve for x
    x = 27,473.06/96
  6. Step 6: Final answer
    x = 286.18

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Why These Related Problems?

These problems maintain the same ratio (1.73) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.