The total cost of 3 pens and 4 pencils is Rs. | vedclass

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Question

(A) Let the cost of one pen be Rs. $x$ and the cost of one pencil be Rs. $y$.According to the problem,we have the following system of linear equations

Vedclass · Accepted Answer

Pen: Rs. $5$,Pencil: Rs. $2$

Vedclass · Answer

(A) Let the cost of one pen be Rs. $x$ and the cost of one pencil be Rs. $y$.According to the problem,we have the following system of linear equations:$3x + 4y = 23$  --- $(1)$$2x + 3y = 16$  --- $(2)$To solve this,multiply equation $(1)$ by $2$ and equation $(2)$ by $3$:$6x + 8y = 46$  --- $(3)$$6x + 9y = 48$  --- $(4)$Subtracting equation $(3)$ from equation $(4)$:$(6x + 9y) - (6x + 8y) = 48 - 46$$y = 2$Substitute $y = 2$ into equation $(1)$:$3x + 4(2) = 23$$3x + 8 = 23$$3x = 15$$x = 5$Therefore,the cost of a pen is Rs. $5$ and the cost of a pencil is Rs. $2$.

The total cost of $3$ pens and $4$ pencils is Rs. $23$ and the total cost of $2$ pens and $3$ pencils is Rs. $16$. Find the cost of a pen and a pencil each.

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