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Finding the Fourth Proportional to 1,382.94, 2,074.65 and 409.10

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Solution

The fourth proportional to 1,382.94, 2,074.65 and 409.10 is: 613.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,382.94 : 2,074.65 = 409.10 : x
  2. Step 2: Convert to fraction form
    1,382.94/2,074.65 = 409.10/x
  3. Step 3: Cross multiply
    1,382.94x = 2,074.65 × 409.10
  4. Step 4: Simplify right side
    1,382.94x = 848,739.32
  5. Step 5: Solve for x
    x = 848,739.32/1,382.94
  6. Step 6: Final answer
    x = 613.72

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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.