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Finding the Third Proportional to 30,971 and 49,219

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Solution

The third proportional to 30,971 and 49,219 is: 78,218.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    30,971 : 49,219 = 49,219 : x
  2. Step 2: Convert to fraction form
    30,971/49,219 = 49,219/x
  3. Step 3: Cross multiply
    30,971x = 49,219 × 49,219
  4. Step 4: Simplify right side
    30,971x = 2,422,509,961
  5. Step 5: Solve for x
    x = 2,422,509,961/30,971
  6. Step 6: Final answer
    x = 78,218.65

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.