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Finding the Fourth Proportional to 75.78, 113.76 and 51.84

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Solution

The fourth proportional to 75.78, 113.76 and 51.84 is: 77.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    75.78 : 113.76 = 51.84 : x
  2. Step 2: Convert to fraction form
    75.78/113.76 = 51.84/x
  3. Step 3: Cross multiply
    75.78x = 113.76 × 51.84
  4. Step 4: Simplify right side
    75.78x = 5,897.32
  5. Step 5: Solve for x
    x = 5,897.32/75.78
  6. Step 6: Final answer
    x = 77.82

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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.