Chapter 6.2, Problem 19P

A shopper purchased 4 tables and 2 chairs for $200 and 2 tables and 7 chairs for $400. What is the cost of each table and each chair?

To determine

To find: The cost of each table and each chair

Answer to Problem 19P

The cost of each table is $25 and the cost of each chair is $50.

Explanation of Solution

Given information:

A shopper purchased 4 tables and 2 chairs for $200 and 2 tables and 7 chairs for $400.

Calculation:

A shopper purchased 4 tables and 2 chairs for $200 and 2 tables and 7 chairs for $400. Let us assume the cost of each table is x and the cost of each chair is y .

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

  $\begin{array}{l}4x+2y=200\\ 2x+7y=400\end{array}$

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

Variables, and plug this into other equation.

  $\begin{array}{l}4x+2y=200\\ 2x+7y=400\end{array}$

As it is given that

  $\begin{array}{l}4x+2y=200\\ \Rightarrow y=100-2x\end{array}$

Now we substitute $y=100-2x$ into $2x+7y=400$ , we get,

  $\begin{array}{l}2x+7y=400\\ \Rightarrow 2x+7(100-2x)=400\\ \Rightarrow 2x+700-14x=400\\ \Rightarrow -12x=-300\\ \Rightarrow x=25\end{array}$

By plugging $x=25$ in equation $y=100-2x$ we get

  $\begin{array}{l}y=100-2x\\ \Rightarrow y=100-2\times 25\\ \Rightarrow y=50\end{array}$

Therefore the solution is

  $\left(x,y\right)=(25,50)$

Therefore the cost of each table is $25 and the cost of each chair is $50.