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Finding the Fourth Proportional to 682.37, 1,023.59 and 410.21

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Solution

The fourth proportional to 682.37, 1,023.59 and 410.21 is: 615.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    682.37 : 1,023.59 = 410.21 : x
  2. Step 2: Convert to fraction form
    682.37/1,023.59 = 410.21/x
  3. Step 3: Cross multiply
    682.37x = 1,023.59 × 410.21
  4. Step 4: Simplify right side
    682.37x = 419,890.44
  5. Step 5: Solve for x
    x = 419,890.44/682.37
  6. Step 6: Final answer
    x = 615.34

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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.