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Finding the Fourth Proportional to 688.27, 1,029.82 and 409.60

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Solution

The fourth proportional to 688.27, 1,029.82 and 409.60 is: 612.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    688.27 : 1,029.82 = 409.60 : x
  2. Step 2: Convert to fraction form
    688.27/1,029.82 = 409.60/x
  3. Step 3: Cross multiply
    688.27x = 1,029.82 × 409.60
  4. Step 4: Simplify right side
    688.27x = 421,810.67
  5. Step 5: Solve for x
    x = 421,810.67/688.27
  6. Step 6: Final answer
    x = 612.86

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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.