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Finding the Fourth Proportional to 409.65, 613.43 and 286.09

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Solution

The fourth proportional to 409.65, 613.43 and 286.09 is: 428.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.65 : 613.43 = 286.09 : x
  2. Step 2: Convert to fraction form
    409.65/613.43 = 286.09/x
  3. Step 3: Cross multiply
    409.65x = 613.43 × 286.09
  4. Step 4: Simplify right side
    409.65x = 175,497.67
  5. Step 5: Solve for x
    x = 175,497.67/409.65
  6. Step 6: Final answer
    x = 428.41

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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.