total price of each item

Question

jim brought 3 shirts and 1 slack for $12.96, jim brought 5 shirts, 3 slacks and 1 coat for $36.91, jim brought 5 shirts and 1 coat for $20.44 what is the cost of each shirt, slack and coat

Answer 1

Let x = the cost of a shirt

Let y = the cost of a slack

Let z = the cost of a coat

 

Using these variables, we can set up equations that represents the total cost for each set.

 

3x + y = 12.96                        eq1

5x + 3y + z = 36.91                eq2

5x + z = 20.44                        eq3

 

 

We have here a system of equations.  Three equations with three variables.  Each equation has the same value of x, y, and z.  To solve system of equations, we use substitution and elimination methods to reduce the number of equations and variables.  This makes is easier to solve for the variables.

 

We can use the substitution method, to get two equations with two variables.  Substitute eq1 into equation eq2.  From eq1,

 

y = 12.96 - 3x

 

 

5x + 3(12.96 - 3x) + z = 36.91

5x + 38.88 - 9x + z = 36.91

 

-4x + z = -1.97                         new eq2

 

 

5x + z = = 20.44                       eq3

 

 

Next, we can subtract eq3 from new eq2 to eliminate the z terms.

 

-9x = -22.41

 

 

Divide both sides of the equation by -9.

 

x = 2.49

 

 

Substitute this value of x into new eq2 to solve for z and eq1 to solve for y.

 

-4(2.49) + z = -1.97

 

-9.96 + z = -1.97

 

            z = 7.99

 

 

y = 12.96 - 3(2.49)

y = 12.96 - 7.47

y = 5.49

 

 

Each shirt costs $2.49

Each slack costs $5.49

Each coat costs $7.99