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Finding the Fourth Proportional to 684.36, 1,024.02 and 410.64

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Solution

The fourth proportional to 684.36, 1,024.02 and 410.64 is: 614.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    684.36 : 1,024.02 = 410.64 : x
  2. Step 2: Convert to fraction form
    684.36/1,024.02 = 410.64/x
  3. Step 3: Cross multiply
    684.36x = 1,024.02 × 410.64
  4. Step 4: Simplify right side
    684.36x = 420,503.57
  5. Step 5: Solve for x
    x = 420,503.57/684.36
  6. Step 6: Final answer
    x = 614.45

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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.