Question

The cost of 2 pants and 3 shirts is $Rs.650$ . If the cost of 4 pants and 2 shirts is $Rs.700$ , find the cost of each pants and shirts.

Answer 1

Hint: To find the cost of each pant and shirt, we will have to make two equations from the given data. Let us consider the cost of a pant to be $x$ and that of a shirt to be $y$ . Since, the cost of 2 pants and 3 shirts is $Rs.650$, we will get the equation $2x+3y=650$ . From the information that the cost of 4 pants and 2 shirts is $Rs.700$ , we will get the equation $4x+2y=700$ . Solving these equations using either substitution or elimination method, the values of $x\text{ and }y$ can be determined.

Complete step by step answer:
It is given that the cost of 2 pants and 3 shirts is $Rs.650$ and the cost of 4 pants and 2 shirts is $Rs.700$ . We have to find the cost of each pant and shirt.
Let us consider the cost of a pant to be $x$ and that of a shirt to be $y$ .
Now, let us form equations from the given data.
From the information that the cost of 2 pants and 3 shirts is $Rs.650$ , we will get the equation below:
$2x+3y=650...(i)$
From the information that the cost of 4 pants and 2 shirts is $Rs.700$ , we will get the equation below:
$4x+2y=700...(ii)$
Let us solve the equations $(i)\text{ and }(ii)$ using elimination method.
For, this, we can multiply equation $(i)$ by 2 for making the coefficient of $x$ to be similar to the one in equation $(ii)$ .
$(i)\Rightarrow 4x+6y=1300...(iii)$
Now, we can subtract equations $(iii)\text{ from }(ii)\text{ }$to eliminate $x$ .
\[\begin{align}
  & \begin{matrix}
   4x & \begin{matrix}
   + & 2y \\
\end{matrix} & = & 700 \\
\end{matrix} \\
 & \begin{matrix}
   4x & \begin{matrix}
   + & 6y \\
\end{matrix} & = & 1300 \\
\end{matrix} \\
 & \begin{matrix}
   - & \text{ }- & {} & \text{ } \\
\end{matrix}\text{ }- \\
 & \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\
 & \begin{matrix}
   \text{ }-4y & \text{ } & =-600 \\
\end{matrix} \\
\end{align}\]

Solving this gives
$y=\dfrac{600}{4}=150$
Now, let us substitute this value in equation $(ii)$ , we will get
$4x+2\times 150=700$
Collecting constants on one side, gives
$4x=700-300$
Let us now solve this.
$\begin{align}
  & 4x=400 \\
 & \Rightarrow x=\dfrac{400}{4}=100 \\
\end{align}$

Hence, the cost of a pant is $Rs.100$ and the cost of a shirt is $Rs.150$.

Note: Be careful when making equations. Do not use - instead of + in the equation $2x+3y=650$ . Also when subtracting two equations, for example equations $(iii)\text{ from }(ii)\text{ }$ , be careful to subtract each term of the equation $(iii)$ , that means, each term changes its sign.
\[\begin{align}
  & \begin{matrix}
   4x & \begin{matrix}
   + & 2y \\
\end{matrix} & = & 700 \\
\end{matrix} \\
 & \begin{matrix}
   4x & \begin{matrix}
   + & 6y \\
\end{matrix} & = & 1300 \\
\end{matrix} \\
 & \begin{matrix}
   - & \text{ }- & {} & \text{ } \\
\end{matrix}\text{ }- \\
 & \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\
 & \begin{matrix}
   \text{ }-4y & \text{ } & =-600 \\
\end{matrix} \\
\end{align}\]
From this, + becomes – and – becomes + for terms in equation $(iii)$ .
The equations can also be solved using substitution method.