Question

The cost of $2$ chairs and $3$ tables is Rs.$800$ and the cost of $4$ chairs and $3$ tables is Rs.$1000$. Find the cost of $2$ chairs and $2$ tables.

Answer 1

Let the cost of one chair be Rs. $x$

the cost of one table be Rs. $y$

Given that:

$2x+3y=800-Eq.\left(1\right)$

and $4x+3y=1000-Eq.\left(2\right)$

To find: $2x+2y$

Now, first of all calculate the value of $x$ and $y$

Subtracting Eq. $\left(2\right)$ from Eq. $\left(1\right)$ we have

$(4x-2x)+(3y-3y)=(1000-800)$

$2x+0=200$

$2x=200$

$x=\frac{200}{2}$

$x=100$

Substituting the value of $x$ in Eq. $\left(1\right)$

$2\left(100\right)+3y=800$

$200+3y=800$

$3y=800-200$

$3y=600$

$y=\frac{600}{3}$

$y=200$

We need to find $2x+2y$

So substituting the calculated values of $x$ and $y$ we have

$=2\left(100\right)+2\left(200\right)$

$=200+400$

$=600$

Hence, the cost of two chairs and two tables is $Rs.600$