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(1)/(2)\text{cups}=(1\cdot2+1)/(2)=(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{(3)/(2)\text{ cups of nuts}}{3\text{ cups of nuts}} \\ 4\cdot3=(3)/(2)\cdot x \\ 12\cdot(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{(2)/(3)\text{ cups of chocolate morsels}}{x\text{ cups of chocolate morsels}}=\frac{(3)/(2)\text{ cups of nuts}}{3\text{ cups of nuts}} \\ (2)/(3)\cdot3=(3)/(2)\cdot x \\ 2\cdot(2)/(3)=x \\ (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{(3)/(2)\text{ cups of nuts}}{3\text{ cups of nuts}} \\ 3\cdot3=(3)/(2)\cdot x \\ 9\cdot(2)/(3)=x \\ 6\text{ cups of oat cereal=x} \end{gathered}`

The total amount is: