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Finding the Third Proportional to 512,274 and 823,085

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Solution

The third proportional to 512,274 and 823,085 is: 1,322,473.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    512,274 : 823,085 = 823,085 : x
  2. Step 2: Convert to fraction form
    512,274/823,085 = 823,085/x
  3. Step 3: Cross multiply
    512,274x = 823,085 × 823,085
  4. Step 4: Simplify right side
    512,274x = 677,468,917,225
  5. Step 5: Solve for x
    x = 677,468,917,225/512,274
  6. Step 6: Final answer
    x = 1,322,473.75

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.