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Finding the Fourth Proportional to 465.24, 697.14 and 411.78

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Solution

The fourth proportional to 465.24, 697.14 and 411.78 is: 617.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    465.24 : 697.14 = 411.78 : x
  2. Step 2: Convert to fraction form
    465.24/697.14 = 411.78/x
  3. Step 3: Cross multiply
    465.24x = 697.14 × 411.78
  4. Step 4: Simplify right side
    465.24x = 287,068.31
  5. Step 5: Solve for x
    x = 287,068.31/465.24
  6. Step 6: Final answer
    x = 617.03

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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.