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Finding the Third Proportional to 263,811 and 409,101

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Solution

The third proportional to 263,811 and 409,101 is: 634,407.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    263,811 : 409,101 = 409,101 : x
  2. Step 2: Convert to fraction form
    263,811/409,101 = 409,101/x
  3. Step 3: Cross multiply
    263,811x = 409,101 × 409,101
  4. Step 4: Simplify right side
    263,811x = 167,363,628,201
  5. Step 5: Solve for x
    x = 167,363,628,201/263,811
  6. Step 6: Final answer
    x = 634,407.32

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.