Question

Souvenir hats, T-shirts, and jackets are sold at a rock concert. Three hats, two T-shirts, and one jacket cost $40. Two hats, two T-shirts, and two jackets cost $60. One hat and three T-shirts cost $10. Find the prices of the individual items. (you have to use substitution and/or elimination method, NO matrix or Graph.)

Answer 1

j = 24

t = 2

h = 4

Explanation:

Three hats, two T-shirts, and one jacket cost $40.

3h + 2t + j = 40

Two hats, two T-shirts, and two jackets cost $60.

2h + 2t + 2j = 60

One hat and three T-shirts cost $10.

h + 3t = 10

3h + 2t + j = 40 (1)

2h + 2t + 2j = 60 (2)

h + 3t = 10. (3)

From (3)

h = 10 - 3t

Substitute into (1) and (2)

3(10 - 3t) + 2t + j = 40 (1)

2(10 - 3t) + 2t + 2j = 60 (2)

30 - 9t + 2t + j = 40

20 - 6t + 2t + 2j = 60

- 7t + j = 40 - 30

-4t + 2j = 60 - 20

-7t + j = 10 (1a)

-4t + 2j = 40 (1b)

Multiply (1a) by 2

-14t + 2j = 20

-4t + 2j = 40

Subtract to eliminate j

-4t - (-14t) = 40 - 20

-4t + 14t = 20

10t = 20

t = 20/10

t = 2

Substitute t = 2 into

h = 10 - 3t

h = 10 - 3(2)

= 10 - 6

= 4

h = 4

Substitute t = 2 and h = 4 into

3h + 2t + j = 40

3(4) + 2(2) + j = 40

12 + 4 + j = 40

16 + j = 40

j = 40 - 16

= 24

j = 24