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Finding the Third Proportional to 1,686 and 2,119

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Solution

The third proportional to 1,686 and 2,119 is: 2,663.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,686 : 2,119 = 2,119 : x
  2. Step 2: Convert to fraction form
    1,686/2,119 = 2,119/x
  3. Step 3: Cross multiply
    1,686x = 2,119 × 2,119
  4. Step 4: Simplify right side
    1,686x = 4,490,161
  5. Step 5: Solve for x
    x = 4,490,161/1,686
  6. Step 6: Final answer
    x = 2,663.20

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Why These Related Problems?

These problems maintain the same ratio (1.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.