How much was she charged for each shirt, each pair of slacks, and each sports coat?

Question

Rachel took clothes to the cleaners three times last month. First, she brought 4 shirts and 1 pair of slacks and paid $9.45. Then she brought 7 shirts, 4 pairs of slacks, and 2 sports coats and paid $40.37. Finally, she bought 5 shirts and 1 sports coat and paid $15. 44. How much was she charged for each shirt, each pair of slacks, and each sports coat?

Answer 1

Let x = shirts, y = slacks, z = sports coats.

Set up your systems of equations equations.

 

Line1: 4x + 1y = $9.45

Line2: 7x + 4y + 2z = $40.37

Line3: 5x + 1z = $15.44

 

Use this system of equations to eliminate y by multiplying Line1 by -4 and adding it with Line2.

Line1: -16x -4y = -37.8

Line2: 7x + 4y + 2z = 40.37

Sum:  -9x + 2z = 2.57

 

 

Take the previous sum and add it to Line3 (which has been multiplied by -2)

Prev Sum:  -9x +2z = 2.57

Line3:        -10x - 2z= -30.88

Sum: -19x = -28.31

 

Solve for x.

x = -28.31/-19 = 1.49

 

Now plug x = 1.49 in Line1 and Simplify.

4(1.49) + 1y = $9.45

Simplify

5.96 + 1y = 9.45

Isolate y

y = 3.49

 

Now plug x and y values into Line2

 

7(1.49) + 4(3.49) + 2z = 40.37

Simplify

24.39 + 2z = 40.37

Isolate z

2z = 15.98

z = 15.98/2 = 7.99

 

Answer:

x = shirts = $1.49

y = pairs of slacks = $3.49

z = sports coat = $7.99

 

 

To check your work, plug back in to the original equations.

Line1: 4x + 1y = $9.45

4(1.49) + 1(3.49) = 9.45  (Perfect!)

Line2: 7x + 4y + 2z = $40.37

7(1.49) + 4(3.49) + 2(7.99) = 40.37 (Perfect!)

Line3: 5x + 1z = $15.44

5(1.49) + 1(7.99) = 15.44 (Perfect!)