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Finding the Fourth Proportional to 683.24, 1,026.78 and 409.40

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Solution

The fourth proportional to 683.24, 1,026.78 and 409.40 is: 615.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    683.24 : 1,026.78 = 409.40 : x
  2. Step 2: Convert to fraction form
    683.24/1,026.78 = 409.40/x
  3. Step 3: Cross multiply
    683.24x = 1,026.78 × 409.40
  4. Step 4: Simplify right side
    683.24x = 420,363.73
  5. Step 5: Solve for x
    x = 420,363.73/683.24
  6. Step 6: Final answer
    x = 615.25

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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.