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Question

Hats, T-shirts, and jackets are sold at ‘Shaggy & Friends’ concert to raise additional funds. Three hats, two T-shirts, and one jacket cost $140. Two hats, two T-shirts, and two jackets cost $170. One hat, three T-shirts, and two jackets cost $180. Use Cramer’s rule the prices of the individual items. Include the following steps:

i.                    Define each variable.

ii.                   Write each equation.

iii.                 Rewrite as systems in matrix form with the coefficient, variables, and constants matrices.

iv.                Calculate each determinant.

v.                  Solve for the price of each item

Answer 1

3 2 1 140

2 2 2 170

1 3 2 180

D = -6 Dx =-90, Dx/D = 15 = price of a Hat

Dy = - 150 Dy/D = 25 = price of a Shirt

Dz = -270 Dz/D = 45 = price of a Jacket

3H + 2S + J = 140

2H + 2S + 2J = 170

H +3S + 2J = 180

H=price of a hat = $15

S = price of a shirt = $25

J = price of a jacket = $45