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Finding the Fourth Proportional to 1,105.43, 1,658.14 and 412.09

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Solution

The fourth proportional to 1,105.43, 1,658.14 and 412.09 is: 618.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,105.43 : 1,658.14 = 412.09 : x
  2. Step 2: Convert to fraction form
    1,105.43/1,658.14 = 412.09/x
  3. Step 3: Cross multiply
    1,105.43x = 1,658.14 × 412.09
  4. Step 4: Simplify right side
    1,105.43x = 683,295.65
  5. Step 5: Solve for x
    x = 683,295.65/1,105.43
  6. Step 6: Final answer
    x = 618.13

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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.