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Finding the Third Proportional to 1,305 and 1,696

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Solution

The third proportional to 1,305 and 1,696 is: 2,204.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,305 : 1,696 = 1,696 : x
  2. Step 2: Convert to fraction form
    1,305/1,696 = 1,696/x
  3. Step 3: Cross multiply
    1,305x = 1,696 × 1,696
  4. Step 4: Simplify right side
    1,305x = 2,876,416
  5. Step 5: Solve for x
    x = 2,876,416/1,305
  6. Step 6: Final answer
    x = 2,204.15

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.