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Finding the Third Proportional to 311,971 and 463,366

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Solution

The third proportional to 311,971 and 463,366 is: 688,230.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    311,971 : 463,366 = 463,366 : x
  2. Step 2: Convert to fraction form
    311,971/463,366 = 463,366/x
  3. Step 3: Cross multiply
    311,971x = 463,366 × 463,366
  4. Step 4: Simplify right side
    311,971x = 214,708,049,956
  5. Step 5: Solve for x
    x = 214,708,049,956/311,971
  6. Step 6: Final answer
    x = 688,230.80

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.