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Finding the Fourth Proportional to 823.04, 1,233.12 and 457.76

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Solution

The fourth proportional to 823.04, 1,233.12 and 457.76 is: 685.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.04 : 1,233.12 = 457.76 : x
  2. Step 2: Convert to fraction form
    823.04/1,233.12 = 457.76/x
  3. Step 3: Cross multiply
    823.04x = 1,233.12 × 457.76
  4. Step 4: Simplify right side
    823.04x = 564,473.01
  5. Step 5: Solve for x
    x = 564,473.01/823.04
  6. Step 6: Final answer
    x = 685.84

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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.