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Finding the Fourth Proportional to 512.69, 769.81 and 409.67

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Solution

The fourth proportional to 512.69, 769.81 and 409.67 is: 615.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    512.69 : 769.81 = 409.67 : x
  2. Step 2: Convert to fraction form
    512.69/769.81 = 409.67/x
  3. Step 3: Cross multiply
    512.69x = 769.81 × 409.67
  4. Step 4: Simplify right side
    512.69x = 315,366.84
  5. Step 5: Solve for x
    x = 315,366.84/512.69
  6. Step 6: Final answer
    x = 615.12

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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.