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Finding the Fourth Proportional to 597.44, 823.59 and 419.85

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Solution

The fourth proportional to 597.44, 823.59 and 419.85 is: 578.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    597.44 : 823.59 = 419.85 : x
  2. Step 2: Convert to fraction form
    597.44/823.59 = 419.85/x
  3. Step 3: Cross multiply
    597.44x = 823.59 × 419.85
  4. Step 4: Simplify right side
    597.44x = 345,784.26
  5. Step 5: Solve for x
    x = 345,784.26/597.44
  6. Step 6: Final answer
    x = 578.78

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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.