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Finding the Fourth Proportional to 683.08, 1,022.10 and 409.24

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Solution

The fourth proportional to 683.08, 1,022.10 and 409.24 is: 612.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    683.08 : 1,022.10 = 409.24 : x
  2. Step 2: Convert to fraction form
    683.08/1,022.10 = 409.24/x
  3. Step 3: Cross multiply
    683.08x = 1,022.10 × 409.24
  4. Step 4: Simplify right side
    683.08x = 418,284.20
  5. Step 5: Solve for x
    x = 418,284.20/683.08
  6. Step 6: Final answer
    x = 612.35

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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.