Question

If a small juice can contain 6 ounces of juice, how many quarts of juice are in a carton that contains 24 small cans?

Answer 1

Hint: We first try to form the proportionality equation for the variables. We take an arbitrary constant. We use the given values of the variables to find the value of the constant. Finally, we put the constant’s value to find the equation along with the unit in quarts.

Complete step by step answer:
We have been given the relation between two variables where we assume volume of juice in a carton as r and number of cans in a carton as p.
The relation between r and p is a direct relation.
It’s given r varies directly as p which gives $r\propto p$.
To get rid of the proportionality we use the proportionality constant which gives $r=kp$.
Here, the number k is the proportionality constant.
It’s given $r=6$ when $p=1$.
We put the values in the equation $r=kp$ to find the value of k.
So, $6=k\times 1$. Simplifying we get \[k=6\].
Therefore, the equation becomes with the value of k as $r=6p$.
Now we simplify the equation to get the value of r for number of cans in a carton being 24
\[\begin{align}
  & r=6p \\
 & \Rightarrow r=6\times 24=144 \\
\end{align}\]
Now we have to change the unit from ounce to quarts. We know 1 quart is equal to 32 ounces. Therefore, 144 ounces is equal to $\dfrac{144}{32}=4.5$ quarts.

Therefore, the volume of juice in the carton is $4.5$ quarts.

Note: The ounce and quart are a unit of measurement for volume and fluid capacity in both the US customary units and the British Imperial systems of measurement. This unit is not used in the normal or common measurement units.