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Finding the Third Proportional to 380,214 and 823,158

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Solution

The third proportional to 380,214 and 823,158 is: 1,782,125.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    380,214 : 823,158 = 823,158 : x
  2. Step 2: Convert to fraction form
    380,214/823,158 = 823,158/x
  3. Step 3: Cross multiply
    380,214x = 823,158 × 823,158
  4. Step 4: Simplify right side
    380,214x = 677,589,092,964
  5. Step 5: Solve for x
    x = 677,589,092,964/380,214
  6. Step 6: Final answer
    x = 1,782,125.57

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.