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Finding the Fourth Proportional to 686, 1,029.72 and 412.40

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Solution

The fourth proportional to 686, 1,029.72 and 412.40 is: 619.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    686 : 1,029.72 = 412.40 : x
  2. Step 2: Convert to fraction form
    686/1,029.72 = 412.40/x
  3. Step 3: Cross multiply
    686x = 1,029.72 × 412.40
  4. Step 4: Simplify right side
    686x = 424,656.53
  5. Step 5: Solve for x
    x = 424,656.53/686
  6. Step 6: Final answer
    x = 619.03

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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.