Souvenir hats, T-shirts, and jackets are sold at a rock concert. 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. Find the prices of the individual items.

Question

24-09-2018
Mathematics

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Souvenir hats, T-shirts, and jackets are sold at a rock concert. 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. Find the prices of the individual items.

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Kamikazeminem Kamikazeminem · Answer 1 · 2018-09-24T23:07:46+02:00

[tex]Let \: x \: be \: the \: price \: of \: a \: hat, \: y \: be \: the \: price \: of \: a \: T-shirt, \: and \: z \: be \: the \: price \: of \: a \: jacket. \: We \: have \: a \: system \: of \: equations: \\ 3x + 2y + z = 140 \\ x + y + z = 85 \\ x + 3y + 2z = 180 \\ x = 15 \\ y = 25 \\ z = 45. \\ So \: the \: price \: of \: a \: hat \: is \: 15, \: a \: T-shirt \: is \: 25 \: and \: a \: jacket \: is \: 45.[/tex]