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Finding the Third Proportional to 311,814 and 456,057

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Solution

The third proportional to 311,814 and 456,057 is: 667,025.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    311,814 : 456,057 = 456,057 : x
  2. Step 2: Convert to fraction form
    311,814/456,057 = 456,057/x
  3. Step 3: Cross multiply
    311,814x = 456,057 × 456,057
  4. Step 4: Simplify right side
    311,814x = 207,987,987,249
  5. Step 5: Solve for x
    x = 207,987,987,249/311,814
  6. Step 6: Final answer
    x = 667,025.81

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.