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Finding the Fourth Proportional to 823, 1,233.26 and 762.24

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Solution

The fourth proportional to 823, 1,233.26 and 762.24 is: 1,142.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    823 : 1,233.26 = 762.24 : x
  2. Step 2: Convert to fraction form
    823/1,233.26 = 762.24/x
  3. Step 3: Cross multiply
    823x = 1,233.26 × 762.24
  4. Step 4: Simplify right side
    823x = 940,040.10
  5. Step 5: Solve for x
    x = 940,040.10/823
  6. Step 6: Final answer
    x = 1,142.21

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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.