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Finding the Third Proportional to 5,826 and 8,419

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Solution

The third proportional to 5,826 and 8,419 is: 12,166.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,826 : 8,419 = 8,419 : x
  2. Step 2: Convert to fraction form
    5,826/8,419 = 8,419/x
  3. Step 3: Cross multiply
    5,826x = 8,419 × 8,419
  4. Step 4: Simplify right side
    5,826x = 70,879,561
  5. Step 5: Solve for x
    x = 70,879,561/5,826
  6. Step 6: Final answer
    x = 12,166.08

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.