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Finding the Third Proportional to 1,706 and 2,102

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Solution

The third proportional to 1,706 and 2,102 is: 2,589.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,706 : 2,102 = 2,102 : x
  2. Step 2: Convert to fraction form
    1,706/2,102 = 2,102/x
  3. Step 3: Cross multiply
    1,706x = 2,102 × 2,102
  4. Step 4: Simplify right side
    1,706x = 4,418,404
  5. Step 5: Solve for x
    x = 4,418,404/1,706
  6. Step 6: Final answer
    x = 2,589.92

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Why These Related Problems?

These problems maintain the same ratio (1.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.