Chapter 6.2, Problem 16P

A shopper purchased 8 T-Shirts and 5 pairs pants for $220. The next day, he purchased 5 T-shirts and 1 pair of pants for $112. How much does each T-shirt and each pair of pants cost?

To determine

To find: The cost of each T-shirt and each pair of pants.

Answer to Problem 16P

The cost of each T-shirt is $20 and the cost of each pair of pants is $12.

Explanation of Solution

Given information:

The cost of each T shirt and each pair of pants cost when a shopper purchased 8 T-shirts and 5 pairs of pants for $220. The next day, he purchased 5 T-shirts and 1 pairs of pants for $112.

Calculation:

Let us assume the cost of each T-shirt is x and the cost of each pair of pants is y .

Hence we can write the above statement in equation form as follows:

  $\begin{array}{l}8x+5y=220\\ 5x+y=112\end{array}$

In order to solve two systems by substitution, we solve one of the equations for one of the

Variables, and plug this into other equation.

  $\begin{array}{l}8x+5y=220\\ 5x+y=112\end{array}$

As it is given that

  $\begin{array}{l}5x+y=112\\ \Rightarrow y=112-5x\end{array}$

Now we substitute $y=112-5x$ into $8x+5y=220$ , we get,

  $\begin{array}{l}8x+5y=220\\ \Rightarrow 8x+5\left(112-5x\right)=220\\ \Rightarrow 8x-25x+560=220\\ \Rightarrow -17x=-340\\ \Rightarrow x=20\end{array}$

By plugging $x=20$ in equation $y=112-5x$ we get

  $\begin{array}{l}y=112-5x\\ \Rightarrow y=112-5\times 20\\ \Rightarrow y=12\end{array}$

Therefore the solution is

  $\left(x,y\right)=(20,12)$