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Finding the Fourth Proportional to 782, 1,078.66 and 502.14

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Solution

The fourth proportional to 782, 1,078.66 and 502.14 is: 692.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    782 : 1,078.66 = 502.14 : x
  2. Step 2: Convert to fraction form
    782/1,078.66 = 502.14/x
  3. Step 3: Cross multiply
    782x = 1,078.66 × 502.14
  4. Step 4: Simplify right side
    782x = 541,638.33
  5. Step 5: Solve for x
    x = 541,638.33/782
  6. Step 6: Final answer
    x = 692.63

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.