Question

You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and two shirts for $84. Your friend buys two pairs of jeans, one pair of shorts, and three shirts for $76. Your cousin buys one pair of jeans, two pairs of shorts, and one shirt for $52. a. Write an augmented matrix to represent the situation. b. Use a graphing calculator to find the cost of each piece of clothing.

Answer 1

We know that

• You buy one pair of jeans, four pairs of shorts, and two shirts for $84.

,

• Your friend buys two pairs of jeans, one pair of shorts, and three shirts for $76.

,

• Your cousin buys one pair of jeans, two pairs of shorts, and one shirt for $52.

Let'ts call x a pair of jeans, y a pair of shorts, and z a pair of shirts.

The system of equations that represent this situation is

`\left\{ \begin{aligned}x+4y+2z=84 \\ 2x+y+3z=76 \\ x+2y+z=52\end{aligned}\right.`

The augmented matrix would be

1 4 2 84

2 1 3 76

1 2 1 52

Using a calculator, the cost of each piece of clothing would be

`\begin{gathered} x=20 \\ y=12 \\ z=8 \end{gathered}`

This means a pair of jeans cost $20, a pair of shorts cost $12, and a shirt costs $8.