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Finding the Third Proportional to 810 and 1,686

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Solution

The third proportional to 810 and 1,686 is: 3,509.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    810 : 1,686 = 1,686 : x
  2. Step 2: Convert to fraction form
    810/1,686 = 1,686/x
  3. Step 3: Cross multiply
    810x = 1,686 × 1,686
  4. Step 4: Simplify right side
    810x = 2,842,596
  5. Step 5: Solve for x
    x = 2,842,596/810
  6. Step 6: Final answer
    x = 3,509.38

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.