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Finding the Third Proportional to 821 and 2,012

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Solution

The third proportional to 821 and 2,012 is: 4,930.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    821 : 2,012 = 2,012 : x
  2. Step 2: Convert to fraction form
    821/2,012 = 2,012/x
  3. Step 3: Cross multiply
    821x = 2,012 × 2,012
  4. Step 4: Simplify right side
    821x = 4,048,144
  5. Step 5: Solve for x
    x = 4,048,144/821
  6. Step 6: Final answer
    x = 4,930.75

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Why These Related Problems?

These problems maintain the same ratio (2.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.