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Finding the Fourth Proportional to 456.41, 684.10 and 209.57

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Solution

The fourth proportional to 456.41, 684.10 and 209.57 is: 314.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.41 : 684.10 = 209.57 : x
  2. Step 2: Convert to fraction form
    456.41/684.10 = 209.57/x
  3. Step 3: Cross multiply
    456.41x = 684.10 × 209.57
  4. Step 4: Simplify right side
    456.41x = 143,366.84
  5. Step 5: Solve for x
    x = 143,366.84/456.41
  6. Step 6: Final answer
    x = 314.12

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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.