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Finding the Third Proportional to 1,786 and 2,102

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Solution

The third proportional to 1,786 and 2,102 is: 2,473.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,786 : 2,102 = 2,102 : x
  2. Step 2: Convert to fraction form
    1,786/2,102 = 2,102/x
  3. Step 3: Cross multiply
    1,786x = 2,102 × 2,102
  4. Step 4: Simplify right side
    1,786x = 4,418,404
  5. Step 5: Solve for x
    x = 4,418,404/1,786
  6. Step 6: Final answer
    x = 2,473.91

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.