To solve this problem, we can set up an equation to determine the maximum number of mini candy bars needed based on the conditions provided.
Let \( x \) be the number of mini candy bars each student receives. Since each of the 8 students can receive no more than 4 mini candy bars, we can express this as:
\[ x \leq 4 \]
The total number of mini candy bars needed for all students would then be represented by:
\[ \text{Total candy bars} = \text{Number of students} \times \text{Candy bars per student} = 8 \times x \]
Substituting the maximum value for \( x \):
\[ \text{Total candy bars} = 8 \times 4 \]
Calculating that gives:
\[ \text{Total candy bars} = 32 \]
So, the equation for the total number of mini candy bars Noah's teacher should buy, given the maximum distribution, is:
\[ \text{Total candy bars} = 8x \quad \text{where} \quad x \leq 4 \]
Thus, if the teacher wants to maximize the number given out, they should buy a total of 32 mini candy bars.
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