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Finding the Fourth Proportional to 686.51, 1,029.78 and 414.35

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Solution

The fourth proportional to 686.51, 1,029.78 and 414.35 is: 621.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.51 : 1,029.78 = 414.35 : x
  2. Step 2: Convert to fraction form
    686.51/1,029.78 = 414.35/x
  3. Step 3: Cross multiply
    686.51x = 1,029.78 × 414.35
  4. Step 4: Simplify right side
    686.51x = 426,684.19
  5. Step 5: Solve for x
    x = 426,684.19/686.51
  6. Step 6: Final answer
    x = 621.53

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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.