Luc baked some cookies. He gave his classmates 3/8 of the cookies. Form the rest, he gave 3/4 to his neighbours. He still has 32 cookies left. How many cookies did Luc have at the beginning?

Answer 1

1 - 3/8 = 8/8 - 3/8 = 5/8 remain after sharing with classmates.

3/4 of 5/8 = 3/4 * 5/8 = 15/32 <--- this is how much he gave to the neighbors

Let N be the number of cookies

N = (3/8)N + (15/32)N + 32

N = (12/32)N + (15/32)N + 32

N = (27/32)N + 32

(32/32)N = (27/32)N + 32

(32/32)N - (27/32)N = 32

(5/32)N = 32

N = 32*32/5

N = 204.8

CHECK:

He shared 3/8 of them with the class....

3/8 of 204.8 = 3*204.8/8 = 76.8 <--- shared with class

204.8-76.8 = 128 remain

He gave 3/4 of 128 to the neighbors.

3/4 * 128 = 3*128/4 = 384/4 = 96 <--- given to neighbors

128 - 96 = 32 remain

204.8 cookies