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Finding the Third Proportional to 1,977 and 2,103

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Solution

The third proportional to 1,977 and 2,103 is: 2,237.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,977 : 2,103 = 2,103 : x
  2. Step 2: Convert to fraction form
    1,977/2,103 = 2,103/x
  3. Step 3: Cross multiply
    1,977x = 2,103 × 2,103
  4. Step 4: Simplify right side
    1,977x = 4,422,609
  5. Step 5: Solve for x
    x = 4,422,609/1,977
  6. Step 6: Final answer
    x = 2,237.03

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Why These Related Problems?

These problems maintain the same ratio (1.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.