Chapter 6.4, Problem 2P

Solve each word problem

During a sale at the local department store, you buy three sweatshirts and two pairs of sweatpants for $85.50. Later you return to the same store and buy three more sweatshirts and four more pairs of sweatpants for $123. What is the sale price of each sweatshirt and each pair of sweatpants?

To determine

To determine the sale price of given items.

Answer to Problem 2P

The price of sweatshirt is $16 and that of pair of sweatpants is $18.75.

Explanation of Solution

Given information :

Price of three sweatshirts and two pairs of sweatpants is $85.50

Price of three sweatshirts and four pairs of sweatpants is $123

Let the price of sweatshirts be x and price of sweatpants be y .

Hence the equation becomes,

  $\begin{array}{l}3x+2y=85.5\\ 3x+4y=123\end{array}$

Now we shall subtract both equations we get,

  $\begin{array}{c}3x+2y-\left(3x+4y\right)=85.5-123\\ \cancel{3x}+2y\cancel{-3x}-4y=-37.5\\ -2y=-37.5\\ y=18.75\end{array}$

Now put the value of y in any equation we get,

  $\begin{array}{l}3x+2\left(18.75\right)=85.5\\ 3x=85.5-37.5\\ 3x=48\\ x=16\end{array}$

Hence the price of sweatshirt is $16 and that of pair of sweatpants is $18.75.