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Finding the Fourth Proportional to 684, 1,025.28 and 410.16

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Solution

The fourth proportional to 684, 1,025.28 and 410.16 is: 614.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    684 : 1,025.28 = 410.16 : x
  2. Step 2: Convert to fraction form
    684/1,025.28 = 410.16/x
  3. Step 3: Cross multiply
    684x = 1,025.28 × 410.16
  4. Step 4: Simplify right side
    684x = 420,528.84
  5. Step 5: Solve for x
    x = 420,528.84/684
  6. Step 6: Final answer
    x = 614.81

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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.