Class 10MathematicsPair of Linear Equations in Two VariablesTextbook - Pair of Linear Equations in Two Variables
MediumForm the pair of linear equations in the following problems,and find their solutions (if they exist) by the elimination method.
Meena went to a bank to withdraw ₹ $2000$. She asked the cashier to give her ₹ $50$ and ₹ $100$ notes only. Meena got $25$ notes in all. Find how many notes of ₹ $50$ and ₹ $100$ she received.
Meena went to a bank to withdraw ₹ $2000$. She asked the cashier to give her ₹ $50$ and ₹ $100$ notes only. Meena got $25$ notes in all. Find how many notes of ₹ $50$ and ₹ $100$ she received.
(A) Let the number of ₹ $50$ notes be $x$ and the number of ₹ $100$ notes be $y$.
According to the given information:
$1$. The total number of notes is $25$,so $x + y = 25$ $...(1)$
$2$. The total value of the notes is ₹ $2000$,so $50x + 100y = 2000$ $...(2)$
To solve by the elimination method,multiply equation $(1)$ by $50$:
$50x + 50y = 1250$ $...(3)$
Subtract equation $(3)$ from equation $(2)$:
$(50x + 100y) - (50x + 50y) = 2000 - 1250$
$50y = 750$
$y = 15$
Substitute $y = 15$ into equation $(1)$:
$x + 15 = 25$
$x = 10$
Therefore,Meena received $10$ notes of ₹ $50$ and $15$ notes of ₹ $100$.
According to the given information:
$1$. The total number of notes is $25$,so $x + y = 25$ $...(1)$
$2$. The total value of the notes is ₹ $2000$,so $50x + 100y = 2000$ $...(2)$
To solve by the elimination method,multiply equation $(1)$ by $50$:
$50x + 50y = 1250$ $...(3)$
Subtract equation $(3)$ from equation $(2)$:
$(50x + 100y) - (50x + 50y) = 2000 - 1250$
$50y = 750$
$y = 15$
Substitute $y = 15$ into equation $(1)$:
$x + 15 = 25$
$x = 10$
Therefore,Meena received $10$ notes of ₹ $50$ and $15$ notes of ₹ $100$.
Explore More
Similar Questions
Use the elimination method to find all possible solutions of the following pair of linear equations:
$2x + 3y = 8$ $...(1)$
$4x + 6y = 7$ $...(2)$
$2x + 3y = 8$ $...(1)$
$4x + 6y = 7$ $...(2)$
Medium
View SolutionWhich of the following pairs of linear equations has a unique solution,no solution,or infinitely many solutions? In case there is a unique solution,find it by using the cross-multiplication method.
$2x + y = 5$
$3x + 2y = 8$
$2x + y = 5$
$3x + 2y = 8$
Difficult
View SolutionSolve the following pair of linear equations by the substitution method.
$3x - y = 3$
$9x - 3y = 9$
$3x - y = 3$
$9x - 3y = 9$
Medium
View SolutionForm the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
The area of a rectangle gets reduced by $9$ square units,if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units,the area increases by $67$ square units. Find the dimensions of the rectangle.
The area of a rectangle gets reduced by $9$ square units,if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units,the area increases by $67$ square units. Find the dimensions of the rectangle.
Medium
View SolutionChampa went to a 'Sale' to purchase some pants and skirts. When her friends asked her how many of each she had bought,she answered,"The number of skirts is two less than twice the number of pants purchased. Also,the number of skirts is four less than four times the number of pants purchased". Help her friends to find how many pants and skirts Champa bought.
Difficult
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo