Question

A carpenter can make maximum $6$ tables or $2$ chairs in a day. Generate the linear equation and find the different combinations of furniture he can make in a day, given that there is no unfinished work at the end of the day.

• A. $6$ tables and no chairs.
• B. $2$ chairs and no tables.
• C. $3$ tables and $1$ chair.
• D. $6$ tables and $2$ chair.

Answer 1

Answer: (A), (B), (C)

$3$ tables and $1$ chair.

Let the number of tables, he manufactured, in 1 day be represented as $x,$

The number of chairs, he manufactured, in 1 day be represented as $y.$

$\therefore$ The linear equation is represented as
$\frac{x}{\text{Maximum tables in 1 day}}+\frac{y}{\text{Maximum chairs in 1 day}}=1$
$\Rightarrow \frac{x}{6}+\frac{y}{2}=1$
(mulitiplying $6$ in both side)
$\Rightarrow x+3y=6$
This the required linear equation.

The number of tables and chairs cannot be negative, and it has to be an integer as per the question.

Also, the carpenter can make maximum $6$ tables or $2$ chairs.
The possible ordered pairs are as follows: $x$ $y$

0	3	6
2	1	0