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Finding the Fourth Proportional to 823.53, 1,232.67 and 457.41

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Solution

The fourth proportional to 823.53, 1,232.67 and 457.41 is: 684.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.53 : 1,232.67 = 457.41 : x
  2. Step 2: Convert to fraction form
    823.53/1,232.67 = 457.41/x
  3. Step 3: Cross multiply
    823.53x = 1,232.67 × 457.41
  4. Step 4: Simplify right side
    823.53x = 563,839.35
  5. Step 5: Solve for x
    x = 563,839.35/823.53
  6. Step 6: Final answer
    x = 684.66

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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.