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Finding the Fourth Proportional to 456.49, 684.80 and 209.64

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Solution

The fourth proportional to 456.49, 684.80 and 209.64 is: 314.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.49 : 684.80 = 209.64 : x
  2. Step 2: Convert to fraction form
    456.49/684.80 = 209.64/x
  3. Step 3: Cross multiply
    456.49x = 684.80 × 209.64
  4. Step 4: Simplify right side
    456.49x = 143,561.47
  5. Step 5: Solve for x
    x = 143,561.47/456.49
  6. Step 6: Final answer
    x = 314.49

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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.