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Finding the Fourth Proportional to 496.64, 684.96 and 409.16

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Solution

The fourth proportional to 496.64, 684.96 and 409.16 is: 564.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    496.64 : 684.96 = 409.16 : x
  2. Step 2: Convert to fraction form
    496.64/684.96 = 409.16/x
  3. Step 3: Cross multiply
    496.64x = 684.96 × 409.16
  4. Step 4: Simplify right side
    496.64x = 280,258.23
  5. Step 5: Solve for x
    x = 280,258.23/496.64
  6. Step 6: Final answer
    x = 564.31

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.