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Finding the Fourth Proportional to 82.15, 123 and 75.77

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Solution

The fourth proportional to 82.15, 123 and 75.77 is: 113.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    82.15 : 123 = 75.77 : x
  2. Step 2: Convert to fraction form
    82.15/123 = 75.77/x
  3. Step 3: Cross multiply
    82.15x = 123 × 75.77
  4. Step 4: Simplify right side
    82.15x = 9,319.71
  5. Step 5: Solve for x
    x = 9,319.71/82.15
  6. Step 6: Final answer
    x = 113.45

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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.