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Finding the Fourth Proportional to 409.14, 564.63 and 234.54

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Solution

The fourth proportional to 409.14, 564.63 and 234.54 is: 323.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.14 : 564.63 = 234.54 : x
  2. Step 2: Convert to fraction form
    409.14/564.63 = 234.54/x
  3. Step 3: Cross multiply
    409.14x = 564.63 × 234.54
  4. Step 4: Simplify right side
    409.14x = 132,428.32
  5. Step 5: Solve for x
    x = 132,428.32/409.14
  6. Step 6: Final answer
    x = 323.67

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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.