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Finding the Fourth Proportional to 731.74, 1,097.63 and 409.16

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Solution

The fourth proportional to 731.74, 1,097.63 and 409.16 is: 613.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    731.74 : 1,097.63 = 409.16 : x
  2. Step 2: Convert to fraction form
    731.74/1,097.63 = 409.16/x
  3. Step 3: Cross multiply
    731.74x = 1,097.63 × 409.16
  4. Step 4: Simplify right side
    731.74x = 449,106.29
  5. Step 5: Solve for x
    x = 449,106.29/731.74
  6. Step 6: Final answer
    x = 613.75

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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.