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 ₹ $100$.
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