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Finding the Fourth Proportional to 688.14, 1,032.75 and 414.54

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Solution

The fourth proportional to 688.14, 1,032.75 and 414.54 is: 622.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    688.14 : 1,032.75 = 414.54 : x
  2. Step 2: Convert to fraction form
    688.14/1,032.75 = 414.54/x
  3. Step 3: Cross multiply
    688.14x = 1,032.75 × 414.54
  4. Step 4: Simplify right side
    688.14x = 428,116.19
  5. Step 5: Solve for x
    x = 428,116.19/688.14
  6. Step 6: Final answer
    x = 622.14

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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.