Question

At the beginning of the bake sale, mary set aside 2 pies for herself. karen then bought half of the remaining pies for her birthday party, and 10 more pies were sold during the sale. when the sale was over, there were 15 pies remaining. how many pies were there before the bake sale started? (hint: work backwards) do not include the word "pies" with your response. provide your answer as a number, only.

Answer 1

52.

Explanation:

Let x be the number of total pies before the bake sale started.

We have been given that at the beginning of the bake sale, Mary set aside 2 pies for herself.

So the pie left for sale will be x-2.

We are also told that Karen bought half of the remaining pies for her birthday party, so number of pies bought by Karen will be:
`(x-2)/(2)`.

Further, we are told that 10 more pies were sold during the sale, so number of total pies sold and used by Mary will be:

`2+(x-2)/(2)+10`

As there were 15 pies remaining, so we can represent total number of pies in an equation as:

`x=2+(x-2)/(2)+10+15`

`x=(x-2)/(2)+27`

Let us have a common denominator.

`x=(x-2)/(2)+(27*2)/(2)`

`x=(x-2)/(2)+(54)/(2)`

`x=(x-2+54)/(2)`

`x=(x+52)/(2)`

Let us multiply both sides of our equation by 2.

`2x=(x+52)/(2)*2`

`2x=x+52`

`2x-x=x-x+52`

`x=52`

Therefore, there were 52 pies before the bake sale started.