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