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Finding the Third Proportional to 31,298 and 68,509

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Solution

The third proportional to 31,298 and 68,509 is: 149,961.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,298 : 68,509 = 68,509 : x
  2. Step 2: Convert to fraction form
    31,298/68,509 = 68,509/x
  3. Step 3: Cross multiply
    31,298x = 68,509 × 68,509
  4. Step 4: Simplify right side
    31,298x = 4,693,483,081
  5. Step 5: Solve for x
    x = 4,693,483,081/31,298
  6. Step 6: Final answer
    x = 149,961.12

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.