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Finding the Fourth Proportional to 821.85, 1,232.31 and 410.77

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Solution

The fourth proportional to 821.85, 1,232.31 and 410.77 is: 615.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    821.85 : 1,232.31 = 410.77 : x
  2. Step 2: Convert to fraction form
    821.85/1,232.31 = 410.77/x
  3. Step 3: Cross multiply
    821.85x = 1,232.31 × 410.77
  4. Step 4: Simplify right side
    821.85x = 506,199.06
  5. Step 5: Solve for x
    x = 506,199.06/821.85
  6. Step 6: Final answer
    x = 615.93

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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.