Q19. - Algebra 2

Question

Carla bought 3 shirts, 4 pairs of pants, and 2 pairs of shoes for a total of \(149.79.Beth bought 5 shirts, 3 pairs of pants, and 3 pairs of shoes totaling \)183.19.Kayla bought 6 shirts, 5 pairs of pants, and a pair of shoes for $181.14. Assume that all of the shirts were the same price, all of the pants were the same price, and all of the shoes were the same price. What was the price of each item?

Step-by-Step Solution

Answer

The price of one shirt is $\$12.95.$

The price of one pant is $\$7.995.$

The price of one pair of shoes is $\$23.49.$

Step 1 – Assume the variables

Let $x$ be the price of one shirt.

Let $y$be the price of one pair of pant.

Let $z$be the price of one pair of shoes.

Step 2 – Formulate the equations with the given data

Carla bought 3 shirts, 4 pairs of pants, and 2 pairs of shoes for a total of $\$149.79.$

$3x+4y+2z=149.79$                                     $....\left(1\right)$

Beth bought 5 shirts, 3 pairs of pants, and 3 pairs of shoes totaling$\$183.19.$

                    $5x+3y+3z=183.19$                 $....\left(2\right)$

Kayla bought 6 shirts, 5 pairs of pants, and a pair of shoes for $\$181.14.$

                      $6x+5y+z=181.14$                      $....\left(3\right)$

Step 3 – Solve the equations, 1 ,   2 and 3

$\begin{array}{c}3x+4y+2z=149.79\\ 5x+3y+3z=183.19\\ 6x+5y+z=181.14\end{array}$

By solving the equations, we get

$\begin{array}{c}x=\frac{259}{20}\\ =\$12.95\end{array}$

The price of one shirt is$\$12.95.$

$\begin{array}{c}y=\frac{1599}{100}\\ =\frac{15.99}{2}\\ =\$7.995\end{array}$

The price of one pant is$\$7.995.$

$\begin{array}{c}z=\frac{2349}{100}\\ =23.49\end{array}$

The price of one pair of shoes is$\$23.49.$