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Finding the Fourth Proportional to 821.75, 1,232.01 and 410.67

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Solution

The fourth proportional to 821.75, 1,232.01 and 410.67 is: 615.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    821.75 : 1,232.01 = 410.67 : x
  2. Step 2: Convert to fraction form
    821.75/1,232.01 = 410.67/x
  3. Step 3: Cross multiply
    821.75x = 1,232.01 × 410.67
  4. Step 4: Simplify right side
    821.75x = 505,949.55
  5. Step 5: Solve for x
    x = 505,949.55/821.75
  6. Step 6: Final answer
    x = 615.70

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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.