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Finding the Third Proportional to 2,037 and 3,197

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Solution

The third proportional to 2,037 and 3,197 is: 5,017.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,037 : 3,197 = 3,197 : x
  2. Step 2: Convert to fraction form
    2,037/3,197 = 3,197/x
  3. Step 3: Cross multiply
    2,037x = 3,197 × 3,197
  4. Step 4: Simplify right side
    2,037x = 10,220,809
  5. Step 5: Solve for x
    x = 10,220,809/2,037
  6. Step 6: Final answer
    x = 5,017.58

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.