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Finding the Third Proportional to 826 and 2,197

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Solution

The third proportional to 826 and 2,197 is: 5,843.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    826 : 2,197 = 2,197 : x
  2. Step 2: Convert to fraction form
    826/2,197 = 2,197/x
  3. Step 3: Cross multiply
    826x = 2,197 × 2,197
  4. Step 4: Simplify right side
    826x = 4,826,809
  5. Step 5: Solve for x
    x = 4,826,809/826
  6. Step 6: Final answer
    x = 5,843.59

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Why These Related Problems?

These problems maintain the same ratio (2.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.