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Finding the Third Proportional to 820 and 1,287

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Solution

The third proportional to 820 and 1,287 is: 2,019.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    820 : 1,287 = 1,287 : x
  2. Step 2: Convert to fraction form
    820/1,287 = 1,287/x
  3. Step 3: Cross multiply
    820x = 1,287 × 1,287
  4. Step 4: Simplify right side
    820x = 1,656,369
  5. Step 5: Solve for x
    x = 1,656,369/820
  6. Step 6: Final answer
    x = 2,019.96

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.