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Finding the Third Proportional to 380 and 1,020

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Solution

The third proportional to 380 and 1,020 is: 2,737.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    380 : 1,020 = 1,020 : x
  2. Step 2: Convert to fraction form
    380/1,020 = 1,020/x
  3. Step 3: Cross multiply
    380x = 1,020 × 1,020
  4. Step 4: Simplify right side
    380x = 1,040,400
  5. Step 5: Solve for x
    x = 1,040,400/380
  6. Step 6: Final answer
    x = 2,737.89

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Why These Related Problems?

These problems maintain the same ratio (2.68) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.