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Finding the Fourth Proportional to 821.68, 1,233.24 and 457.24

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Solution

The fourth proportional to 821.68, 1,233.24 and 457.24 is: 686.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    821.68 : 1,233.24 = 457.24 : x
  2. Step 2: Convert to fraction form
    821.68/1,233.24 = 457.24/x
  3. Step 3: Cross multiply
    821.68x = 1,233.24 × 457.24
  4. Step 4: Simplify right side
    821.68x = 563,886.66
  5. Step 5: Solve for x
    x = 563,886.66/821.68
  6. Step 6: Final answer
    x = 686.26

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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.