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Finding the Fourth Proportional to 821.80, 1,231.62 and 411.40

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Solution

The fourth proportional to 821.80, 1,231.62 and 411.40 is: 616.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    821.80 : 1,231.62 = 411.40 : x
  2. Step 2: Convert to fraction form
    821.80/1,231.62 = 411.40/x
  3. Step 3: Cross multiply
    821.80x = 1,231.62 × 411.40
  4. Step 4: Simplify right side
    821.80x = 506,688.47
  5. Step 5: Solve for x
    x = 506,688.47/821.80
  6. Step 6: Final answer
    x = 616.56

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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.