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Finding the Third Proportional to 2,037 and 3,213

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Solution

The third proportional to 2,037 and 3,213 is: 5,067.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,037 : 3,213 = 3,213 : x
  2. Step 2: Convert to fraction form
    2,037/3,213 = 3,213/x
  3. Step 3: Cross multiply
    2,037x = 3,213 × 3,213
  4. Step 4: Simplify right side
    2,037x = 10,323,369
  5. Step 5: Solve for x
    x = 10,323,369/2,037
  6. Step 6: Final answer
    x = 5,067.93

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.