Questions: A snack shack sells trail mix packs and bottles of water during a softball game. The items are not sold individually. Instead, the snack shack only sells a "Snack Special" that contains 2 packs of trail mix and 3 bottles of water. Complete the table using equivalent ratios. Trail mix packs 2 4 20 Bottles of water 3 18 Vivian scored 8 out of 10 on a quiz. Ramona scored 3 out of 4. Did Vivian and Ramona get equivalent scores? Explain.

Solution Steps

The "Snack Special" contains 2 packs of trail mix and 3 bottles of water. To fill in the table, we use the ratio $2:3$ (trail mix packs to bottles of water).

1. For the second column, the number of trail mix packs is 4. Since $2 \times 2 = 4$, the number of bottles of water is $3 \times 2 = 6$.
2. For the third column, the number of bottles of water is 18. Since $3 \times 6 = 18$, the number of trail mix packs is $2 \times 6 = 12$.
3. For the fourth column, the number of trail mix packs is 20. Since $2 \times 10 = 20$, the number of bottles of water is $3 \times 10 = 30$.

The completed table is:

\begin{tabular}{|l|l|l|l|l|} \hline Trail mix packs & 2 & 4 & 12 & 20 \\ \hline Bottles of water & 3 & 6 & 18 & 30 \\ \hline \end{tabular}

Vivian scored $8$ out of $10$, which simplifies to $\frac{8}{10} = \frac{4}{5}$.
Ramona scored $3$ out of $4$, which simplifies to $\frac{3}{4}$.

To check if the scores are equivalent, compare $\frac{4}{5}$ and $\frac{3}{4}$. Since $\frac{4}{5} = 0.8$ and $\frac{3}{4} = 0.75$, the scores are not equivalent.

Final Answer