Question

in each package there are 12 boxes. and each box there are six jars. which number completes the equation that relates p the number of packages in j the number of jars? j = __ p

Answer 1

6 jars = 1 box

12 box = 1 package

Let jars be "j", boxes be "b", and packages be "p". So, we can write:

$\begin{gathered} 6j=1b \\ 12b=1p \end{gathered}$

We need "j" in terms of "p", so we substitute however we can.

Putting first equation into 2nd, we get:

$\begin{gathered} 6j=1b \\ b=6j \\ \text{Now, we have:} \\ 12b=p \\ \text{Substituting,} \\ 12(6j)=p \\ 72j=p \end{gathered}$

This tells us that there are 72 jars is a whole package.

Re-arranging the equation to solve for j, we have:

$\begin{gathered} 72j=p \\ j=\frac{p}{72} \\ j=\frac{1}{72}p \end{gathered}$

Answer:

$j=\frac{1}{72}p$