Question

How much of each ingredient would you need to make a hundred quarts of punch

Answer 1

Let's define the next variables:

x: quarts of sparkling water

y: quarts of grape juice

We want to make 100 quarts of punch, then

x + y = 100

In order to follow the recipe we need to keep the next ratio:

`\begin{gathered} (x)/(y)=(1(1)/(2))/((3)/(4)) \\ (x)/(y)=(1.5)/(0.75) \\ (x)/(y)=2 \\ \text{Isolating x} \\ x=2y \end{gathered}`

Replacing this result into the first equation:

`\begin{gathered} 2y+y=100 \\ 3y=100 \\ y=(100)/(3) \\ y=33(1)/(3) \end{gathered}`

Replacing into the previous formula:

`\begin{gathered} x=2y \\ x=2\cdot33(1)/(3) \\ x=66(2)/(3) \end{gathered}`

You would need 66 2/3 quarts of sparkling water and 33 1/3 quarts of grape juice to make 100 quarts of punch