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Finding the Fourth Proportional to 523, 721.86 and 412.84

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Solution

The fourth proportional to 523, 721.86 and 412.84 is: 569.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 721.86 = 412.84 : x
  2. Step 2: Convert to fraction form
    523/721.86 = 412.84/x
  3. Step 3: Cross multiply
    523x = 721.86 × 412.84
  4. Step 4: Simplify right side
    523x = 298,012.68
  5. Step 5: Solve for x
    x = 298,012.68/523
  6. Step 6: Final answer
    x = 569.81

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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.