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.

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.
Transcript text: 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. \begin{tabular}{|l|l|l|l|l|} \hline Trail mix packs & 2 & 4 & & 20 \\ \hline Bottles of water & 3 & & 18 & \\ \hline \end{tabular} Vivian scored 8 out of 10 on a quiz. Ramona scored 3 out of 4. Did Vivian and Ramona get equivalent scores? Explain.
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Solution

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Solution Steps

Step 1: Complete the table using equivalent ratios

The "Snack Special" contains 2 packs of trail mix and 3 bottles of water. To fill in the table, we use the ratio 2:32:3 (trail mix packs to bottles of water).

  1. For the second column, the number of trail mix packs is 4. Since 2×2=42 \times 2 = 4, the number of bottles of water is 3×2=63 \times 2 = 6.
  2. For the third column, the number of bottles of water is 18. Since 3×6=183 \times 6 = 18, the number of trail mix packs is 2×6=122 \times 6 = 12.
  3. For the fourth column, the number of trail mix packs is 20. Since 2×10=202 \times 10 = 20, the number of bottles of water is 3×10=303 \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}

Step 2: Compare Vivian's and Ramona's scores

Vivian scored 88 out of 1010, which simplifies to 810=45\frac{8}{10} = \frac{4}{5}.
Ramona scored 33 out of 44, which simplifies to 34\frac{3}{4}.

To check if the scores are equivalent, compare 45\frac{4}{5} and 34\frac{3}{4}. Since 45=0.8\frac{4}{5} = 0.8 and 34=0.75\frac{3}{4} = 0.75, the scores are not equivalent.

Final Answer

  1. 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}

  1. Vivian and Ramona did not get equivalent scores because 4534\frac{4}{5} \neq \frac{3}{4}.
    \\(\boxed{\text{Vivian and Ramona did not get equivalent scores.}}\\)
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