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Finding the Third Proportional to 211,461 and 311,349

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Solution

The third proportional to 211,461 and 311,349 is: 458,421.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    211,461 : 311,349 = 311,349 : x
  2. Step 2: Convert to fraction form
    211,461/311,349 = 311,349/x
  3. Step 3: Cross multiply
    211,461x = 311,349 × 311,349
  4. Step 4: Simplify right side
    211,461x = 96,938,199,801
  5. Step 5: Solve for x
    x = 96,938,199,801/211,461
  6. Step 6: Final answer
    x = 458,421.17

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.