Mathematics
Form the pair of linear equations in the following problem, 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.
Linear Equations
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Answer
Let no. of ₹ 50 notes be x and no. of ₹ 100 notes be y.
Given,
Meena got 25 notes in all.
x + y = 25 ……..(1)
Given,
Total money = ₹ 2000
⇒ 50x + 100y = 2000
⇒ 50(x + 2y) = 2000
⇒ x + 2y =
⇒ x + 2y = 40 ………(2)
Subtracting equation (1) from (2), we get :
⇒ x + 2y - (x + y) = 40 - 25
⇒ x - x + 2y - y = 15
⇒ y = 15.
Substituting value of y in equation (1), we get :
⇒ x + 15 = 25
⇒ x = 25 - 15 = 10.
Hence, pair of linear equations are x + 2y = 40, x + y = 25, where x and y are respectively the number of ₹50 and ₹100 notes; x = 10, y = 15.
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