Question

At the deli, two smoked turkey subs and five veggie subs cost $29. Four smoked turkey subs and three veggie subs cost $30. (A) Create a linear system to model the equations. (B) Solve the system to determine the cost of a smoked turkey sub and the cost of a veggie sub.

Answer 1

For this case, the first thing we must do is define variables.
 We have then:
 x: cost of smoked turkey
 y: cost of veggie subs
 By writing the system of equations we have:
 $2x + 5y = 29 4x + 3y = 30$
 Resolving the system graphically we have the solution is:
 $x = 4.5 y = 4$
 See attached image for the graphic solution: You must observe the point of intersection of the lines.
 Answer:
 smoked turkey = 4.5 $
 veggie sub = 4 $

Answer 2

The linear system that models the considered situation well is $2x + 5y = 29\\4x + 3y = 30$

The costs for both food items are given as:

• The cost of one turkey sub = $x = $4.5
• The cost of one veggie sub = $y = $4
  

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the considered case, we can assume the cost to be defined by two variables.

Let we assume:

• Cost of smoked turkey subs = $\ x$
• Cost of veggie subs = $\ y$

Then, according to the given situation, we get:

cost of two smoked turkey + cost of five veggie subs = $29

or

$2x + 5y = 29$

Cost of four smoked turkey subs + cost of three veggie subs = $30

or

$4x + 3y = 30$

Thus, we get two linear equations in two variables. They form a system of linear equations modelling the situation considered.

$2x + 5y = 29\\4x + 3y = 30$

How to find the solution to the given system of equation?

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

For the given case, trying the method of substitution, we will use the first equation to get the expression for variable x in terms of y.

We get:

$2x + 5y = 29\\\\x = \dfrac{29-5y}{2}$

Putting this value in second equation, we get:

$4x + 3y = 30\\\\4(\dfrac{29-5y}{2}) + 3y = 30\\\\58 -10y +3y = 30\\\\28= 7y\\\\y = \dfrac{28}{7} = 4$

Putting this value in the expression we got for x, we get:

$x = \dfrac{29-5y}{2} = \dfrac{29 - 5 \times 4}{2} = 4.5$

Thus, the cost of one turkey sub = $x = $4.5

The cost of one veggie sub = $y = $4

Thus, the linear system that models the considered situation well is $2x + 5y = 29\\4x + 3y = 30$

The costs for both food items are given as:

• The cost of one turkey sub = $x = $4.5
• The cost of one veggie sub = $y = $4

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