Question

Jada and Diego bakes a large batch of cookies

They select 1/4 of the cookies to give to their teachers
Next, they threw away one burnt cookie
They delivered 2/5 of the remaining cookies to a local nursing home
Next, they have 3 cookies to some neighborhood kids
They wrapped up 2/3 of the remaining cookies to save for their friends
After all this, they had 15 cookies left. How many cookie did they bake

Answer 1

They baked 108 cookies

Explanation:

Assume that Jada and Diego baked x cookies

∵ Jada and Diego baked x cookies

∵ They select
`(1)/(4)` of the cookies to give to their teachers

∴ They give their teachers =
`(1)/(4)` × x =
`(1)/(4)` x

- Find the remaining cookies

∴ The remaining cookies = x -
`(1)/(4)` x =
`(3)/(4)` x

∵ They threw away one burnt cookie

∴ The remaining cookies =
`(3)/(4)` x - 1

∵ They delivered
`(2)/(5)` of the remaining cookies to a local nursing home

- That means the new remaining will be
`(3)/(5)` of the old remaining

∴ The new remaining =
`(3)/(5)` (
`(3)/(4)` x - 1) =
`(9)/(20)` x -
`(3)/(5)`

∵ They gave 3 cookies to some neighborhood kids

∴ The next remaining =
`(9)/(20)` x -
`(3)/(5)` - 3

- Add the like terms

∴ The next remaining =
`(9)/(20)` x -
`(18)/(5)`

∵ They wrapped up
`(2)/(3)` of the remaining cookies to save for their friends

- That means the last remaining will be
`(1)/(3)` of the previous remaining

∴ The last remaining =
`(1)/(3)` (
`(9)/(20)` x -
`(18)/(5)` )

∴ The last remaining =
`(3)/(20)` x -
`(6)/(5)`

∵ They had 15 cookies left

- Equate the last remaining by 15 to find x

∴
`(3)/(20)` x -
`(6)/(5)` = 15

- Add
`(6)/(5)` to both terms

∴
`(3)/(20)` x =
`(81)/(5)`

- Divide both sides by
`(3)/(20)`

∴ x = 108

They baked 108 cookies