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.

I need to work on this with someone

Question

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. 

I need to work on this with someone

anonymous · Answer

So we need variables for our unknowns.  Let them be $t, c, v$ for turkey, chicken, and vegetable respectively.

We know $2c=v$ since there are twice as many chicken plates as veggie plates.
Can you think of any other equations we have?

anonymous · Answer

oops I meant $c=2v$

anonymous · Answer

yea so we do
$$t+c+v=6$$$$2v+v+t=3.4(6)$$

anonymous · Answer

oh wait

anonymous · Answer

$$t+v+2v=6$$$$4.8t+1.2(2v)=3.4(6)$$

anonymous · Answer

$t+c+v=6$ is correct.
$c+v+t = 3.4(6)$ is incorrect.  We need prices for all of them!

anonymous · Answer

is that right?

anonymous · Answer

The second one should be:

$4.8t + 2.4c + 1.2v = 3.4(6)$

Ummm try not to substitute until you have all your equations or you'll start confusing me, lol

anonymous · Answer

lol sorry

anonymous · Answer

and then we substitute for the c's right?

anonymous · Answer

Yeah

anonymous · Answer

k thanks wio! :D

anonymous · Answer

You can always check your solutions here: http://www.wolframalpha.com/input/?i=c%3D2v%2C+t%2Bc%2Bv%3D6%2C+4.8t%2B2.4c%2B1.2v%3D3.4%286%29