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Finding the Third Proportional to 77 and 129.75

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Solution

The third proportional to 77 and 129.75 is: 218.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    77 : 129.75 = 129.75 : x
  2. Step 2: Convert to fraction form
    77/129.75 = 129.75/x
  3. Step 3: Cross multiply
    77x = 129.75 × 129.75
  4. Step 4: Simplify right side
    77x = 16,835.06
  5. Step 5: Solve for x
    x = 16,835.06/77
  6. Step 6: Final answer
    x = 218.64

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Why These Related Problems?

These problems maintain the same ratio (1.69) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.