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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. K
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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?
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Mathematics
4 years
2021-08-05T20:03:36+00:00
2021-08-05T20:03:36+00:00 1 Answers
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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