Answer:
Let's define the variables:
M = cost of a meat
C = cost of a cheese.
V = cost of a veggetal.
Assuming that the cost of the subs only depends on the thins they order.
We know that:
" Vicki chooses 1 meat, 2 cheeses and 5 veggies for her sub and paid $5.70."
M + 2*C + 5*V = $5.70
"Jamal paid $7.85 and got 3 meats, 2 cheeses and 2 veggies on his sub. "
3*M + 2*C + 2*V = $7.85
"Tyson ordered 2 meats, 1 cheese and 4 veggies and paid $6.15 for his sub."
2*M + 1*C + 4*V = $6.15
Then we have a system of 3 equations and 3 variables:
M + 2*C + 5*V = $5.70
3*M + 2*C + 2*V = $7.85
2*M + 1*C + 4*V = $6.15
The first step to solve this is isolate one of the variables in one of the equations, and then replace that in the other two.
I will isolate M in the first equation:
M = $5.70 - 2*C - 5*V
Replacing that in the other two equations we get;
3*($5.70 - 2*C - 5*V) + 2*C + 2*V = $7.85
2*($5.70 - 2*C - 5*V) + 1*C + 4*V = $6.15
Let's simplify the equations:
$17.10 - 4*C - 13*V = $7.85
$11.40 - 3*C - 6*V = $6.15
Now let's isolate other of the variables, i will isolate C in the second one:
3*C = -6*V + $11.40 - $6.15 = $5.25
C = -2*V + $1.75
Now let's replace that in the other equation and get:
$17.10 - 4*(-2*V + $1.75) - 13*V = $7.85
Now we can solve this for V:
$17.10 + 8*V - $7 - 13*V = $7.85
$10.10 - 5*V = $7.85
5*V = $10.10 - $7.85 = $2.25
V = $2.25/5 = $0.45
Now we can find the other two costs:
C = -2*$0.45 + $2.625 = $0.85
M = $5.70 - 2*$0.85 - 5*$0.45 = $1.75
Now we can answer the question:
"How much would a sub that had 4 meats, 2 cheeses and 3 veggies cost?"
4*$1.75 + 2*$0.85 + 3*$0.45 = $10.50
The sub will cost $10.50
