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Finding the Third Proportional to 826 and 1,109

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Solution

The third proportional to 826 and 1,109 is: 1,488.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    826 : 1,109 = 1,109 : x
  2. Step 2: Convert to fraction form
    826/1,109 = 1,109/x
  3. Step 3: Cross multiply
    826x = 1,109 × 1,109
  4. Step 4: Simplify right side
    826x = 1,229,881
  5. Step 5: Solve for x
    x = 1,229,881/826
  6. Step 6: Final answer
    x = 1,488.96

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.