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Finding the Third Proportional to 5,198 and 6,314

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Solution

The third proportional to 5,198 and 6,314 is: 7,669.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,198 : 6,314 = 6,314 : x
  2. Step 2: Convert to fraction form
    5,198/6,314 = 6,314/x
  3. Step 3: Cross multiply
    5,198x = 6,314 × 6,314
  4. Step 4: Simplify right side
    5,198x = 39,866,596
  5. Step 5: Solve for x
    x = 39,866,596/5,198
  6. Step 6: Final answer
    x = 7,669.60

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.