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Finding the Fourth Proportional to 180.65, 270.78 and 77.84

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Solution

The fourth proportional to 180.65, 270.78 and 77.84 is: 116.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    180.65 : 270.78 = 77.84 : x
  2. Step 2: Convert to fraction form
    180.65/270.78 = 77.84/x
  3. Step 3: Cross multiply
    180.65x = 270.78 × 77.84
  4. Step 4: Simplify right side
    180.65x = 21,079.06
  5. Step 5: Solve for x
    x = 21,079.06/180.65
  6. Step 6: Final answer
    x = 116.69

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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.