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Finding the Third Proportional to 416 and 1,082

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Solution

The third proportional to 416 and 1,082 is: 2,814.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    416 : 1,082 = 1,082 : x
  2. Step 2: Convert to fraction form
    416/1,082 = 1,082/x
  3. Step 3: Cross multiply
    416x = 1,082 × 1,082
  4. Step 4: Simplify right side
    416x = 1,170,724
  5. Step 5: Solve for x
    x = 1,170,724/416
  6. Step 6: Final answer
    x = 2,814.24

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Why These Related Problems?

These problems maintain the same ratio (2.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.