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Finding the Fourth Proportional to 582.32, 872.12 and 409.16

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Solution

The fourth proportional to 582.32, 872.12 and 409.16 is: 612.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    582.32 : 872.12 = 409.16 : x
  2. Step 2: Convert to fraction form
    582.32/872.12 = 409.16/x
  3. Step 3: Cross multiply
    582.32x = 872.12 × 409.16
  4. Step 4: Simplify right side
    582.32x = 356,836.62
  5. Step 5: Solve for x
    x = 356,836.62/582.32
  6. Step 6: Final answer
    x = 612.78

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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.