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Finding the Third Proportional to 2,082 and 3,215

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Solution

The third proportional to 2,082 and 3,215 is: 4,964.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,082 : 3,215 = 3,215 : x
  2. Step 2: Convert to fraction form
    2,082/3,215 = 3,215/x
  3. Step 3: Cross multiply
    2,082x = 3,215 × 3,215
  4. Step 4: Simplify right side
    2,082x = 10,336,225
  5. Step 5: Solve for x
    x = 10,336,225/2,082
  6. Step 6: Final answer
    x = 4,964.57

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.