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Finding the Fourth Proportional to 1,382.81, 2,074.34 and 409.19

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Solution

The fourth proportional to 1,382.81, 2,074.34 and 409.19 is: 613.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,382.81 : 2,074.34 = 409.19 : x
  2. Step 2: Convert to fraction form
    1,382.81/2,074.34 = 409.19/x
  3. Step 3: Cross multiply
    1,382.81x = 2,074.34 × 409.19
  4. Step 4: Simplify right side
    1,382.81x = 848,789.84
  5. Step 5: Solve for x
    x = 848,789.84/1,382.81
  6. Step 6: Final answer
    x = 613.82

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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.