Respuesta :
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 [tex] \frac{2}{3} [/tex] of orginally made cookies
So its [tex] \frac{2}{3} * x [/tex]
[tex] \frac{2}{3} [/tex] is sold so she is left with [tex] \frac{1}{3} [/tex] of cookies
She gave 1/5 of the remainder to her friends
So its [tex] \frac{1}{5} [/tex] * [tex] \frac{1}{3} * x [/tex]
She gave [tex] \frac{1}{15}* x [/tex] to her friends
she had 60 cookies left
Number of cookies = cookies sold + cookies gave to friends + cookies left
x = [tex] \frac{2}{3} * x + \frac{1}{15} * x + 60 [/tex]
Take common denominator and combine like terms
x = [tex] \frac{10}{15} * x + \frac{1}{15} * x + 60 [/tex]
x = [tex] \frac{11}{15} * x + 60 [/tex]
[tex] \frac{-11}{15} * x + x = 60 [/tex]
[tex] \frac{4}{15} * x = 60 [/tex]
Multiply by 15 on both sides
[tex] 4x = 900 [/tex]
Divide by 4 from both sides
[tex] x = 225 [/tex]
She originally made 225 cookies
