The relationship between the number of people (n) who received gum and the number of pieces of gum each person receives (p) can be represented by the table:
\[ \begin{array} \hline n & p \\ \hline 1 & 180 \\ 2 & 90 \\ 3 & 60 \\ 4 & 45 \\ 5 & 36 \\ 6 & 30 \\ \hline \end{array} \]
To determine the relationship between the number of people (n) who received gum and the number of pieces of gum each person receives ((p), we can use the formula
. This formula represents the division of the total number of gum pieces (180) by the number of people (n). The resulting table shows the values of (p) for various values of (n). For example, when (n = 1), each person receives all 180 pieces of gum, and as (n) increases, the number of pieces each person receives (p) decreases proportionally.
The table provided demonstrates the inverse relationship between (n) and (p). As (n) increases, (p) decreases, reflecting the idea that more people sharing the same quantity of gum results in fewer pieces for each person. This relationship is essential for Jackson to ensure an equitable distribution of gum among his friends. The table offers a clear representation of how the number of pieces each person receives depends on the number of people sharing the gum.