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Finding the Third Proportional to 77 and 82

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Solution

The third proportional to 77 and 82 is: 87.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    77 : 82 = 82 : x
  2. Step 2: Convert to fraction form
    77/82 = 82/x
  3. Step 3: Cross multiply
    77x = 82 × 82
  4. Step 4: Simplify right side
    77x = 6,724
  5. Step 5: Solve for x
    x = 6,724/77
  6. Step 6: Final answer
    x = 87.32

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Why These Related Problems?

These problems maintain the same ratio (1.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.