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Finding the Fourth Proportional to 823.22, 1,233.84 and 412.46

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Solution

The fourth proportional to 823.22, 1,233.84 and 412.46 is: 618.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.22 : 1,233.84 = 412.46 : x
  2. Step 2: Convert to fraction form
    823.22/1,233.84 = 412.46/x
  3. Step 3: Cross multiply
    823.22x = 1,233.84 × 412.46
  4. Step 4: Simplify right side
    823.22x = 508,909.65
  5. Step 5: Solve for x
    x = 508,909.65/823.22
  6. Step 6: Final answer
    x = 618.19

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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.