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Finding the Third Proportional to 123 and 165.75

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Solution

The third proportional to 123 and 165.75 is: 223.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    123 : 165.75 = 165.75 : x
  2. Step 2: Convert to fraction form
    123/165.75 = 165.75/x
  3. Step 3: Cross multiply
    123x = 165.75 × 165.75
  4. Step 4: Simplify right side
    123x = 27,473.06
  5. Step 5: Solve for x
    x = 27,473.06/123
  6. Step 6: Final answer
    x = 223.36

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.