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Finding the Fourth Proportional to 686.43, 1,029.65 and 456.80

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Solution

The fourth proportional to 686.43, 1,029.65 and 456.80 is: 685.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.43 : 1,029.65 = 456.80 : x
  2. Step 2: Convert to fraction form
    686.43/1,029.65 = 456.80/x
  3. Step 3: Cross multiply
    686.43x = 1,029.65 × 456.80
  4. Step 4: Simplify right side
    686.43x = 470,336.69
  5. Step 5: Solve for x
    x = 470,336.69/686.43
  6. Step 6: Final answer
    x = 685.19

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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.