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Finding the Fourth Proportional to 821.54, 1,231.67 and 410.47

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Solution

The fourth proportional to 821.54, 1,231.67 and 410.47 is: 615.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    821.54 : 1,231.67 = 410.47 : x
  2. Step 2: Convert to fraction form
    821.54/1,231.67 = 410.47/x
  3. Step 3: Cross multiply
    821.54x = 1,231.67 × 410.47
  4. Step 4: Simplify right side
    821.54x = 505,563.58
  5. Step 5: Solve for x
    x = 505,563.58/821.54
  6. Step 6: Final answer
    x = 615.39

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.