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Finding the Third Proportional to 397,106 and 856,416

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Solution

The third proportional to 397,106 and 856,416 is: 1,846,983.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    397,106 : 856,416 = 856,416 : x
  2. Step 2: Convert to fraction form
    397,106/856,416 = 856,416/x
  3. Step 3: Cross multiply
    397,106x = 856,416 × 856,416
  4. Step 4: Simplify right side
    397,106x = 733,448,365,056
  5. Step 5: Solve for x
    x = 733,448,365,056/397,106
  6. Step 6: Final answer
    x = 1,846,983.84

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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.