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Finding the Fourth Proportional to 597.18, 823.64 and 410.42

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Solution

The fourth proportional to 597.18, 823.64 and 410.42 is: 566.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    597.18 : 823.64 = 410.42 : x
  2. Step 2: Convert to fraction form
    597.18/823.64 = 410.42/x
  3. Step 3: Cross multiply
    597.18x = 823.64 × 410.42
  4. Step 4: Simplify right side
    597.18x = 338,038.33
  5. Step 5: Solve for x
    x = 338,038.33/597.18
  6. Step 6: Final answer
    x = 566.06

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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.