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Finding the Third Proportional to 2,082 and 2,442

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Solution

The third proportional to 2,082 and 2,442 is: 2,864.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,082 : 2,442 = 2,442 : x
  2. Step 2: Convert to fraction form
    2,082/2,442 = 2,442/x
  3. Step 3: Cross multiply
    2,082x = 2,442 × 2,442
  4. Step 4: Simplify right side
    2,082x = 5,963,364
  5. Step 5: Solve for x
    x = 5,963,364/2,082
  6. Step 6: Final answer
    x = 2,864.25

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.