Answer: pastel: $2
brush: $1
canvas: $4
Explanation:
Let P = price of pastels, B = price of brushes, and C = price of canvases.
Write a system of equations to represent the data in the table.
5P + 3B + 2C = 21 Isela's purchases
2P + 4B + 3C = 20 Richard's purchases
3P + 2B + 6C = 32 Elizabeth's purchases
Eliminate one variable.
3(5P + 3B + 2C = 21) → 15P + 9B + 6C= 63 Multiply the first equation by 3.
− (3P + 2B + 6C= 32)
12P + 7B = 31 Subtract.
2(2P + 4B + 3C = 20) → 4P + 8B + 6C= 40 Multiply the second equation by 2.
− (3P + 2B + 6C= 32)
P + 6B = 8 Subtract.
Write the 2-by-2 system.
12P + 7B = 31
12P + 6B = 8
Eliminate P, and solve for B.
12(P + 6B = 8)→ 12P + 72B= 96 Multiply the second equation by 12.
− (12P + 7B= 31)
65B = 65 Subtract.
B= 1 Divide both sides by 65.
Use one of the equations in the 2-by-2 system to solve for P.
P + 6B= 8
P + 6(1) = 8 Substitute 1 for B.
P= 2 Subtract 6 from both sides.
Substitute for P and B in one of the original equations to solve for C.
5P + 3B + 2C= 21
5(2) + 3(1) + 2C = 21 Substitute 2 for P and 1 for B.
10 + 3 + 2C = 21 Multiply.
2C + 13 = 21 Simplify.
2C= 8 Subtract 13 from both sides.
C= 4 Divide both sides by 2.
The solution to the system is (2, 1, 4). Therefore, pastels cost $2, brushes cost $1, and canvases cost $4.