Finding Number of ₹1 and ₹2 Coins
Video Explanation
Question
Aruna has only ₹1 and ₹2 coins. The total number of coins is 50 and the total amount is ₹75. Find the number of ₹1 and ₹2 coins respectively.
Solution
Step 1: Assume Variables
Let number of ₹1 coins = \(x\)
Let number of ₹2 coins = \(y\)
Step 2: Form Equations
Total coins:
\[ x + y = 50 \quad (1) \]
Total value:
\[ x + 2y = 75 \quad (2) \]
Step 3: Solve Equations
Subtract (1) from (2):
\[ (x + 2y) – (x + y) = 75 – 50 \]
\[ y = 25 \]
Substitute in (1):
\[ x + 25 = 50 \Rightarrow x = 25 \]
Step 4: Final Values
₹1 coins = 25
₹2 coins = 25
Final Answer
\[ (25,\; 25) \]