Chapter 11, Problem 28CT

To determine

To find: The price of each clothing item.

Answer to Problem 28CT

The price of 1 pair of jeans was $24.5, 1 camisoles was $8.5 and 1 T-Shirts was $6

Explanation of Solution

Given: Megan went clothes shopping and bought 2 pairs of flare jeans, 2 camisoles and 4 T shirts for $90.00. AT same store, Paige bought one pair of flare jeans and 3 T shirts for $42.50 while Kara bought 1 pair of flare jeans, 3 camisoles and 2 T shirts for $62.00.

Let the cost of 1 pair of flare jeans be $\$x$

Let the cost of 1 camisoles be $\$y$

Let the cost of 1 T-Shirts be $\$z$

According to question,

  $\begin{array}{c}2x+2y+4z=90.00\\ x+3z=42.50\\ x+3y+2z=62.00\end{array}$

Solve system of equation by elimination method,

  $\begin{array}{c}\begin{array}{c}2x+2y+4z=90.00\\ x+3y+2z=62.00\end{array}]\begin{array}{c}\times 3\\ \times -2\end{array}\\ 6x+6y+12z=270\\ -2x-6y-4z=-124\\ 4x+8z=146\\ 2x+4z=73\end{array}$

Now, taking $x+3z=42.50\text{ and }2x+4z=73$

  $\begin{array}{c}x+3z=42.50]\times -2\\ 2x+4z=73\\ -2x-6z=-85\\ 2x+4z=73\\ -2z=-12\\ z=6\end{array}$

Put $z=6$ in $x+3z=42.50$

  $\begin{array}{c}x+3\left(6\right)=42.50\\ x=24.5\end{array}$

Put $x=24.5\text{ and }z=6\text{ in }x+3y+2z=62$

  $\begin{array}{c}24.5+3y+2\left(6\right)=62\\ y=8.5\end{array}$

Hence, the price of 1 pair of jeans was $24.5, 1 camisoles was $8.5 and 1 T-Shirts was $6