"We eat the same meals."
Translation:Nous mangeons les mêmes repas.
There's a bit of a nuance to the placement of adjectives (that I'm yet to pick up on). There's more information here http://french.about.com/od/grammar/a/adjectives_4.htm. It seems that adjectives before the noun have a figurative meaning, whereas adjectives after the noun have a literal meaning.
So here même is placed before the noun because we aren't literally eating the same meal off the same plate, but we've perhaps ordered the same thing at a restaurant.
When used as an adjective (in the sense of 'same'), 'même' comes before the noun. You just have to remember this because it obviously doesn't fit in the BANGS scheme. For example: Il veut la même chose = He wants the same thing.
Of course, 'meme' can be used in many different senses. One very common use is in the formation of the pronouns 'myself', himself' etc. For example: moi-meme = myself, lui-même = himself, elle-même = herself, vous-même = yourself (plural or formal), elles-mêmes = themselves (feminine), eux-mêmes = themselves (masculine)...