Question

Jermaine, Keira, and Leon are buying supplies for an art class. Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushes for $34. Keira spent $22 on 1 canvas, 3 tubes of paint, and 1 paint brush. Leon already has plenty of paint, so he bought 3 canvases and 2 paint brushes for $17. How much did each type of material cost?​

Answer 1

Answer:

canvas $3

tube of paint $5

paint brush $4

Step-by-step explanation:

We need to choose variables for the prices of the different items, translate the sentences into equations, and solve a system of equations.

1. Define variables

Let c = price of 1 canvas, t = price of 1 tube of paint, and b = price of 1 brush.

2. Translate sentences into equations

"Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushes for $34."

2c + 4t + 2b = 34

"Keira spent $22 on 1 canvas, 3 tubes of paint, and 1 paint brush."

c + 3t + b = 22

"Leon already has plenty of paint, so he bought 3 canvases and 2 paint brushes for $17."

3c + 2b = 17

The system of equations is

2c + 4t + 2b = 34       Eq. 1

c + 3t + b = 22           Eq. 2

3c + 2b = 17               Eq. 3

Since the third equation has only the variables c and b, we use the first equations to eliminate variable t and give us an equation in only c and b.

3 * Eq. 1 - 4 * Eq. 2

2c + 2b = 14

c + b = 7            Eq. 4

Eq. 3 and Eq. 4 form a system of equations in two variables.

3c + 2b = 17      Eq. 3

c + b = 7          Eq. 4

Solve Eq. 4 for b.

b = 7 - c        Eq. 5

Substitute into Eq. 3.

3c + 2(7 - c) = 17

3c + 14 - 2c = 17

c = 3

Plug in c = 3 into Eq. 5.

b = 7 - 3

b = 4

Plug in c = 3 and b = 3 into Eq. 2.

c + 3t + b = 22           Eq. 2

3 + 3t + 4 = 22

3t + 7 = 22

3t = 15

t = 5

Answer:

canvas $3

tube of paint $5

paint brush $4