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Finding the Third Proportional to 822 and 2,211

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Solution

The third proportional to 822 and 2,211 is: 5,947.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    822 : 2,211 = 2,211 : x
  2. Step 2: Convert to fraction form
    822/2,211 = 2,211/x
  3. Step 3: Cross multiply
    822x = 2,211 × 2,211
  4. Step 4: Simplify right side
    822x = 4,888,521
  5. Step 5: Solve for x
    x = 4,888,521/822
  6. Step 6: Final answer
    x = 5,947.11

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Why These Related Problems?

These problems maintain the same ratio (2.69) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.