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Finding the Fourth Proportional to 82, 123 and 51.78

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Solution

The fourth proportional to 82, 123 and 51.78 is: 77.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    82 : 123 = 51.78 : x
  2. Step 2: Convert to fraction form
    82/123 = 51.78/x
  3. Step 3: Cross multiply
    82x = 123 × 51.78
  4. Step 4: Simplify right side
    82x = 6,368.94
  5. Step 5: Solve for x
    x = 6,368.94/82
  6. Step 6: Final answer
    x = 77.67

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.