Set x = chocolate mint, y = green mint

"The ratio of chocolate mints to green mints in a bag is 3:5" => (x/y) = (3/5) => 5x - 3y = 0 (1)

"After John ate half of the green mints and only one chocolate mint, the ratio of chocolate mint to green mint was 7:6"

=> (x - 1) / (y / 2) = (7 / 6) => 6x - (7/2)y = 6 (2)

solve the (1) and (2) as a set of equation

Then, x = 36, y = 60

Mint are left in the bag = (36 - 1) + (60/2) = 35 + 30 = 75 mints :)