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Finding the Third Proportional to 1,991 and 3,182

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Solution

The third proportional to 1,991 and 3,182 is: 5,085.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,991 : 3,182 = 3,182 : x
  2. Step 2: Convert to fraction form
    1,991/3,182 = 3,182/x
  3. Step 3: Cross multiply
    1,991x = 3,182 × 3,182
  4. Step 4: Simplify right side
    1,991x = 10,125,124
  5. Step 5: Solve for x
    x = 10,125,124/1,991
  6. Step 6: Final answer
    x = 5,085.45

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.