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Finding the Fourth Proportional to 864, 1,296.16 and 408

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Solution

The fourth proportional to 864, 1,296.16 and 408 is: 612.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    864 : 1,296.16 = 408 : x
  2. Step 2: Convert to fraction form
    864/1,296.16 = 408/x
  3. Step 3: Cross multiply
    864x = 1,296.16 × 408
  4. Step 4: Simplify right side
    864x = 528,833.28
  5. Step 5: Solve for x
    x = 528,833.28/864
  6. Step 6: Final answer
    x = 612.08

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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.