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Finding the Third Proportional to 822 and 1,311

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Solution

The third proportional to 822 and 1,311 is: 2,090.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    822 : 1,311 = 1,311 : x
  2. Step 2: Convert to fraction form
    822/1,311 = 1,311/x
  3. Step 3: Cross multiply
    822x = 1,311 × 1,311
  4. Step 4: Simplify right side
    822x = 1,718,721
  5. Step 5: Solve for x
    x = 1,718,721/822
  6. Step 6: Final answer
    x = 2,090.90

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.