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Finding the Fourth Proportional to 597.29, 824.02 and 410.90

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Solution

The fourth proportional to 597.29, 824.02 and 410.90 is: 566.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    597.29 : 824.02 = 410.90 : x
  2. Step 2: Convert to fraction form
    597.29/824.02 = 410.90/x
  3. Step 3: Cross multiply
    597.29x = 824.02 × 410.90
  4. Step 4: Simplify right side
    597.29x = 338,584.67
  5. Step 5: Solve for x
    x = 338,584.67/597.29
  6. Step 6: Final answer
    x = 566.87

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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.