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She needs a score of 81 on the fourth quiz to have an average of 80.
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To answer this question, we need to use the linear equation:

We all know that to get the average using the mean, we add all the terms and then, divide it by the number of terms.

Okay, let x be the least score she can make in the 4th quiz:
        \frac{81 + 76 + 82 + x}{4}    \geq  80

The symbol "  \geq " means at least and  \leq means at most.

Okay, we add terms that can be added, so we first add 81, 76, and 82.

  \frac{81 + 76 + 82 + x}{4} \geq 80

It becomes: 
  \frac{ 239 + x}{4} \geq 80

We multiply 4 to both sides to cancel the denominator 
 \frac{239 + x}{4} x 4 = 239 + x
80 x 4 =320

So, it is:
                239 + x  \geq  320

We subtract 239 to both sides so that only thing that will be left in "239 + x" is only "x." 
             239 + x -  239  \geq  320 - 239
              x  \geq  81

Therefore, the least score she can make on the 4th quiz is 81.

Answer:  81

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