MULTI$-$STEP Michelle and Julie work at a catering company. They need to bake $264$ cookies for a birthday party that starts in a little over an hour and a half. Each tube of cookie dough claims to make $36$ cookies, but Michelle eats about $\frac{1}{5}$ of every tube and Julie makes cookies that are $1\mathrm{.}5$ times as large as the recommended cookie size. It takes about $8$ minutes to bake a container of cookies, but since Julie's cookies are larger, they take $12$ minutes to bake.

a$.$ How many tubes should each girl plan to bake? How long does each girl use the oven?

b$.$ Explain your solution process.

c$.$ What assumptions did you make?