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Finding the Third Proportional to 77.63 and 178.88

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Solution

The third proportional to 77.63 and 178.88 is: 412.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    77.63 : 178.88 = 178.88 : x
  2. Step 2: Convert to fraction form
    77.63/178.88 = 178.88/x
  3. Step 3: Cross multiply
    77.63x = 178.88 × 178.88
  4. Step 4: Simplify right side
    77.63x = 31,996.27
  5. Step 5: Solve for x
    x = 31,996.27/77.63
  6. Step 6: Final answer
    x = 412.19

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.