Question

At the beginning of the bake sale merry set aside two pies for herself Kate bought half of the remaining pies for a birthday party and 10 more pies were sold during the sale. When the sale was over were 14 pies remaining how many pies were there before the bake sale started

Answer 1

so.. .at the beginning of the sale, there was a total of "x" pies

now, let's see what happened to those pies

`\bf \begin{array}{lrlll} &pies\\\\ &\textendash\textendash\textendash\textendash\textendash\textendash&\\ Mary&x-2\\\\ Kate&\cfrac{x-2}{2}\\\\ \textit{pies sold}&10\\\\ \textit{pies leftover}&14 \end{array}`

so, we had "x"
then Mary took 2, she left x - 2
Kate took half of that (x-2)/2
then 10 were sold, and 14 leftover

if we subtract all those figures, and solve for "x",
we should get what "x" was, so
`\bf (x-2)-\left( \cfrac{x-2}{2} \right)-10-14=0`

notice, if we subtract what Mary took, and Kate, and the sold and leftover, from the original "x", we would end up with no pies :)

so.. just solve for "x"