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Finding the Fourth Proportional to 824.25, 1,233.79 and 457.86

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Solution

The fourth proportional to 824.25, 1,233.79 and 457.86 is: 685.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    824.25 : 1,233.79 = 457.86 : x
  2. Step 2: Convert to fraction form
    824.25/1,233.79 = 457.86/x
  3. Step 3: Cross multiply
    824.25x = 1,233.79 × 457.86
  4. Step 4: Simplify right side
    824.25x = 564,900.58
  5. Step 5: Solve for x
    x = 564,900.58/824.25
  6. Step 6: Final answer
    x = 685.35

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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.