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Finding the Third Proportional to 821 and 2,162

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Solution

The third proportional to 821 and 2,162 is: 5,693.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    821 : 2,162 = 2,162 : x
  2. Step 2: Convert to fraction form
    821/2,162 = 2,162/x
  3. Step 3: Cross multiply
    821x = 2,162 × 2,162
  4. Step 4: Simplify right side
    821x = 4,674,244
  5. Step 5: Solve for x
    x = 4,674,244/821
  6. Step 6: Final answer
    x = 5,693.35

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Why These Related Problems?

These problems maintain the same ratio (2.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.