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Finding the Third Proportional to 512,284 and 823,100

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Solution

The third proportional to 512,284 and 823,100 is: 1,322,496.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    512,284 : 823,100 = 823,100 : x
  2. Step 2: Convert to fraction form
    512,284/823,100 = 823,100/x
  3. Step 3: Cross multiply
    512,284x = 823,100 × 823,100
  4. Step 4: Simplify right side
    512,284x = 677,493,610,000
  5. Step 5: Solve for x
    x = 677,493,610,000/512,284
  6. Step 6: Final answer
    x = 1,322,496.13

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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.