A cafeteria serves three choices for lunch: turkey, chicken, or veggie. The turkey plate costs $4.80, the chicken plate costs $2.40, and the vegetable plate costs $1.20. If the lunches are mixed making 6 orders for $3.40 each, with twice as many chicken plates as veggie plates, find the number of each lunch plate mixed. Provide the answer along with an explanation of how you arrived at the answer.

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