Question

In this discussion, you will be creating your own application problems that your fellow classmates will solve using systems of linear equations. Let’s first look at an example. When creating an application problem, it is helpful to begin with the solution to the problem.

So, for example, if you start with the solutions (a rectangular garden with width = 8 ft, length = 10 ft), then you must find two ways these quantities relate to each other and give this information as clues in the problem statement. In this case, the two ways are with the perimeter = 36 ft, and the fact that the length is 2 ft longer than the width). So, your problem statement would be:

"Find the width and length of a rectangular garden if the length is two feet longer than the width and the perimeter is 36 feet."

Remember that we are dealing with systems of linear equations. That means you cannot use area or volume formulas, since those are nonlinear, meaning that they contain squared and cubed variables, respectively.

Now, let's begin our discussion of application problemsinvolving systems of linear equations.

• Formulate two application (real-world) problems that can be solved with a system of equations in either 2 or 3 variables. Check your problem statements to make sure they include all of the information necessary to write down the governing system of equations.
• Using your problem statements, set up and solve the system of equations for each of your two problems yourself.
• Save the solutions and use them to respond to those who reply to your problems.
• Post your two problems in the discussion board:
• • Give the problem statement only.
  • Do NOT give the system of equations needed to solve the problem or the solution.

Answer 1

The two problems involving linear equations in two variables along with their procedure of solving and their solutions are given below which can be used on the discussion board

Problem 1

John went to a bank to withdraw $2000 he asked the cashier to give the cash in $50 and $100 notes only he got 25 notes in all. How many notes of each denomination did he recieve ?

Solution :

We can setup the linear equations as follows

Let the number of $50 notes be ;

Let the number of $100 notes be ;

then,

and

Henry used the substitution method.

From equation (1)

Substituting in equation (2)

Problem 2

7 chairs and 4 tables for a classroom cost $7000 while 5 chairs and three tables cost $5080. Find the cost of one chair and one table seperately.

Solution:

Let the cost of one cahir =

and 1 table costs $5,

Then 7 chair cost   and 4 table costs

The total cost of 7 chairs and 4 tables is given as

(1)

and the cost of 5 chairs and 3 tables is given as

(2)

On multiplying (i) by 3 (ii) by 4 and subtracting, we get  

On substituting in (i), we get :

Cost of each chair = $680 and cost of each table =$560

THE ABOVE TWO PROBLEMS WHICH DESCRIBES THE LINEAR EQUATIONS SYSTEM IN TWO VARIABLES CAN BE USED FOR THE DISCUSSSION BOARD