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Finding the Fourth Proportional to 596.16, 823.08 and 409.59

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Solution

The fourth proportional to 596.16, 823.08 and 409.59 is: 565.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    596.16 : 823.08 = 409.59 : x
  2. Step 2: Convert to fraction form
    596.16/823.08 = 409.59/x
  3. Step 3: Cross multiply
    596.16x = 823.08 × 409.59
  4. Step 4: Simplify right side
    596.16x = 337,125.34
  5. Step 5: Solve for x
    x = 337,125.34/596.16
  6. Step 6: Final answer
    x = 565.49

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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.