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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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.

Similar Questions

Solve the following pairs of equations by the method of elimination:
$5(x-2) + 3y = 1$
$3(x+1) + 5(y-3) = 1$

Solve the following pairs of equations by the method of elimination:
$4x - 3y = 5$
$\frac{5}{2}x - y = 4$

Use the method of elimination to find the solution of the following pair of linear equations: $2x + y = 4$ and $x + 3y = 7$.

Solve the following pairs of equations by the method of elimination:
$\frac{x}{2} + \frac{3y}{5} + 1 = 0$
$\frac{x}{2} + \frac{y}{3} - \frac{1}{3} = 0$

Solve the following pair of linear equations by the method of elimination: $2x + 5y = 7$ and $4x + 10y = 12$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module