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Finding the Fourth Proportional to 82.14, 123.24 and 47.84

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Solution

The fourth proportional to 82.14, 123.24 and 47.84 is: 71.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    82.14 : 123.24 = 47.84 : x
  2. Step 2: Convert to fraction form
    82.14/123.24 = 47.84/x
  3. Step 3: Cross multiply
    82.14x = 123.24 × 47.84
  4. Step 4: Simplify right side
    82.14x = 5,896.11
  5. Step 5: Solve for x
    x = 5,896.11/82.14
  6. Step 6: Final answer
    x = 71.78

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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.