Question

Emily made a batch of cookies. She sold 2/3 of them and gave 1/5 of the remainder to her friends. If she had 60 cookies left, how many cookies did she originally make?

Answer 1

1/5 of 60 is 12 so she gave 12 cookies to her friends

Answer 2

She sold 2/3 of them and gave 1/5 of the remainder to her friends.

Let x = the number of cookies she originally make

She sold
`(2)/(3)` of orginally made cookies

So its
`(2)/(3) * x`

`(2)/(3)` is sold so she is left with
`(1)/(3)` of cookies

She gave 1/5 of the remainder to her friends

So its
`(1)/(5)` *
`(1)/(3) * x`

She gave
`(1)/(15)* x` to her friends

she had 60 cookies left

Number of cookies = cookies sold + cookies gave to friends + cookies left

x =
`(2)/(3) * x + (1)/(15) * x + 60`

Take common denominator and combine like terms

x =
`(10)/(15) * x + (1)/(15) * x + 60`

x =
`(11)/(15) * x + 60`

`(-11)/(15) * x + x = 60`

`(4)/(15) * x = 60`

Multiply by 15 on both sides

`4x = 900`

Divide by 4 from both sides

`x = 225`

She originally made 225 cookies