Chapter 1.4, Problem 18E

To determine

The price of each piece of furniture.

Answer to Problem 18E

Cost of sofa is $\$800$ , cost of love seat is $\$500$ and cost of chair is $\$300$ .

Explanation of Solution

Given information: Three combination of furniture are given.

Calculation: let $x$ represent cost of one sofa, $y$ represent cost of one love seat and $z$ represent cost of one chair.

Set up a system of three equations:

  $\begin{array}{l}x+y=1300(i)\\ x+2z=1400(ii)\\ x+y+z=1600(iii)\end{array}$

Subtract equation $(i)\mathrm{from}(iii)$ we get:

  $\begin{array}{l}x+y+z=1600\\ x+2z=1400\\ ---\\ \overline{y-z=200}(iv)\end{array}$

Subtract equation $(ii)\mathrm{from}(iii)$ we get:

  $\begin{array}{l}x+y+z=1600\\ x+y=1300\\ ----\\ \overline{z=300}\\ \mathrm{put}z=300\mathrm{in}\mathrm{equation}(iv)\\ y-300=200\\ y=200+300\\ y=500\\ \mathrm{put}z=300\mathrm{and}y=500\mathrm{in}\mathrm{equation}(iii)\\ x+500+300=1600\\ x=1600-500-300\\ x=800\end{array}$

Therefore cost of sofa is $\$800$ , cost of love seat is $\$500$ and cost of chair is $\$300$ .