Linear Equation

Question

A man spent P1500.00 for one pair of socks, one shirt and one pair of slacks. He found that twice the cost of a pair of socks less three times the cost of the shirt plus thrice the cost of the pair of slacks would have resulted in his spending only P800.00. He also observed that thrice the cost of a pair of socks less the cost of the shirt plus twice the cost of the slacks would cost him P1300.00. What is the cost of each clothing?

Answer 1

Let x = price of a pair socks, y = price of a shirt and z = price of one pair slacks.

x+y+z=1500

2x-3y+3z=800

3x-y+2z=1300

Since this is Linear Algebra, let's put this into a matrix

[1 1 1 1500]

[2 -3 3 800]

[3 -1 2 1300]

R2 = R2-2R1

R3 = R3-3R1

[1 1 1 1500]

[0 -5 1 -2200]

[0 -4 -1 -3200]

R2 = R2/5

[1 1 1 1500]

[0 -1 1/5 -440]

[0 -4 -1 -3200]

R3 = R3 -4R2

[1 1 1 1500]

[0 -1 1/5 -440]

[0 0 -9/5 -1440]

R3 = -5/9R3

[1 1 1 1500]

[0 -1 1/5 -440]

[0 0 1 800]

Back substituting

z = 800

-y + 160 = 440 --> y = 600

x + 600 + 800 = 1500 --> x = 100

Socks are P100.00

Shirts are P600.00

Slacks are P800.00