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Finding the Fourth Proportional to 514.73, 709.08 and 409.78

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Solution

The fourth proportional to 514.73, 709.08 and 409.78 is: 564.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    514.73 : 709.08 = 409.78 : x
  2. Step 2: Convert to fraction form
    514.73/709.08 = 409.78/x
  3. Step 3: Cross multiply
    514.73x = 709.08 × 409.78
  4. Step 4: Simplify right side
    514.73x = 290,565.03
  5. Step 5: Solve for x
    x = 290,565.03/514.73
  6. Step 6: Final answer
    x = 564.51

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.