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Finding the Fourth Proportional to 1,286.97, 1,930.49 and 409.48

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Solution

The fourth proportional to 1,286.97, 1,930.49 and 409.48 is: 614.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,286.97 : 1,930.49 = 409.48 : x
  2. Step 2: Convert to fraction form
    1,286.97/1,930.49 = 409.48/x
  3. Step 3: Cross multiply
    1,286.97x = 1,930.49 × 409.48
  4. Step 4: Simplify right side
    1,286.97x = 790,497.05
  5. Step 5: Solve for x
    x = 790,497.05/1,286.97
  6. Step 6: Final answer
    x = 614.23

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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.