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Finding the Fourth Proportional to 82.24, 123.96 and 77.84

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Solution

The fourth proportional to 82.24, 123.96 and 77.84 is: 117.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    82.24 : 123.96 = 77.84 : x
  2. Step 2: Convert to fraction form
    82.24/123.96 = 77.84/x
  3. Step 3: Cross multiply
    82.24x = 123.96 × 77.84
  4. Step 4: Simplify right side
    82.24x = 9,649.05
  5. Step 5: Solve for x
    x = 9,649.05/82.24
  6. Step 6: Final answer
    x = 117.33

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.