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Finding the Third Proportional to 123 and 177.84

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Solution

The third proportional to 123 and 177.84 is: 257.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    123 : 177.84 = 177.84 : x
  2. Step 2: Convert to fraction form
    123/177.84 = 177.84/x
  3. Step 3: Cross multiply
    123x = 177.84 × 177.84
  4. Step 4: Simplify right side
    123x = 31,628.40
  5. Step 5: Solve for x
    x = 31,628.40/123
  6. Step 6: Final answer
    x = 257.14

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.