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Finding the Fourth Proportional to 731.68, 1,097.54 and 409.10

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Solution

The fourth proportional to 731.68, 1,097.54 and 409.10 is: 613.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    731.68 : 1,097.54 = 409.10 : x
  2. Step 2: Convert to fraction form
    731.68/1,097.54 = 409.10/x
  3. Step 3: Cross multiply
    731.68x = 1,097.54 × 409.10
  4. Step 4: Simplify right side
    731.68x = 449,003.61
  5. Step 5: Solve for x
    x = 449,003.61/731.68
  6. Step 6: Final answer
    x = 613.66

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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.