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Finding the Fourth Proportional to 597.24, 823.64 and 410.94

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Solution

The fourth proportional to 597.24, 823.64 and 410.94 is: 566.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    597.24 : 823.64 = 410.94 : x
  2. Step 2: Convert to fraction form
    597.24/823.64 = 410.94/x
  3. Step 3: Cross multiply
    597.24x = 823.64 × 410.94
  4. Step 4: Simplify right side
    597.24x = 338,464.57
  5. Step 5: Solve for x
    x = 338,464.57/597.24
  6. Step 6: Final answer
    x = 566.71

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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.