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Finding the Third Proportional to 311,968 and 463,364

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Solution

The third proportional to 311,968 and 463,364 is: 688,231.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    311,968 : 463,364 = 463,364 : x
  2. Step 2: Convert to fraction form
    311,968/463,364 = 463,364/x
  3. Step 3: Cross multiply
    311,968x = 463,364 × 463,364
  4. Step 4: Simplify right side
    311,968x = 214,706,196,496
  5. Step 5: Solve for x
    x = 214,706,196,496/311,968
  6. Step 6: Final answer
    x = 688,231.47

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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.