Question

Celia is making two snack mixes for a party. Her recipes are shown in the table. If each snack mix contains 3 cups of nuts, which mix has the greater total quantity?

Answer 1

$1\frac{1}{2}\text{cups}=\frac{1\cdot2+1}{2}=\frac{3}{2}\text{cups}$

Popcorn mix

3/2 cups of nuts are related to 4 cups of popcorn, To calculate how many cups of popcorn are related to 3 cups of nuts, we can use the next proportion:

$\begin{gathered} \frac{4\text{ cups of popcorn}}{x\text{ cups of popcorn}}=\frac{\frac{3}{2}\text{ cups of nuts}}{3\text{ cups of nuts}} \\ 4\cdot3=\frac{3}{2}\cdot x \\ 12\cdot\frac{2}{3}=x \\ 8\text{ cups of popcorn=x} \end{gathered}$

3/2 cups of nuts are related to 2/3 cups of chocolate morsels, To calculate how many cups of morsels are related to 3 cups of nuts, we can use the next proportion:

$\begin{gathered} \frac{\frac{2}{3}\text{ cups of chocolate morsels}}{x\text{ cups of chocolate morsels}}=\frac{\frac{3}{2}\text{ cups of nuts}}{3\text{ cups of nuts}} \\ \frac{2}{3}\cdot3=\frac{3}{2}\cdot x \\ 2\cdot\frac{2}{3}=x \\ \frac{4}{3}\text{ cups of chocolate morsels=x} \end{gathered}$

3/2 cups of nuts are related to 3 cups of oat cereal, To calculate how many cups of oat cereal are related to 3 cups of nuts, we can use the next proportion:

$\begin{gathered} \frac{\text{3 cups of oat cereal}}{x\text{ cups of oat cereal}}=\frac{\frac{3}{2}\text{ cups of nuts}}{3\text{ cups of nuts}} \\ 3\cdot3=\frac{3}{2}\cdot x \\ 9\cdot\frac{2}{3}=x \\ 6\text{ cups of oat cereal=x} \end{gathered}$

The total amount is:

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