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Finding the Fourth Proportional to 465.86, 644.28 and 409.16

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Solution

The fourth proportional to 465.86, 644.28 and 409.16 is: 565.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    465.86 : 644.28 = 409.16 : x
  2. Step 2: Convert to fraction form
    465.86/644.28 = 409.16/x
  3. Step 3: Cross multiply
    465.86x = 644.28 × 409.16
  4. Step 4: Simplify right side
    465.86x = 263,613.60
  5. Step 5: Solve for x
    x = 263,613.60/465.86
  6. Step 6: Final answer
    x = 565.86

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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.