Question

Vicki, Jamal and Tyson are ordering subs from a shop that lets them choose the number of

Answer 1

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