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I have a total of $\ Rs. 300$ in coins of denominations $\ Rs. 1,\ Rs. 2$ and $\ Rs. 5$. The number of $\ Rs. 2$ coins is 3 times the number of $\ Rs. 5$ coins. The total number of coins is 160. How many coins of each denomination are with me?
The total number of coins $= 160$.
Sum total of all coins $= Rs. 300$.
Coins are in the denomination $\ Rs. 1, \ Rs. 2,$ and $\ Rs. 5$.
The number of $\ Rs. 2$ coins is 3 times the number of $\ Rs. 5$ coins.
To do :
We have to find the number of coins in each denomination.
Let the number of Rs. 1 coins be x and the number of Rs. 5 coins be y.
The number of Rs. 2 coins is 3 times the number of Rs. 5 coins.
The number of Rs. 2 coins $= 3y$.
$[x(1)+3y(2)+y(5)] = Rs. 300$
Subtract equation (i) from equation (ii).
Substituting $y=20$ in equation (i),
The number of Rs. 1 coins is 80, Rs. 2 coins is 3(20)$=$60, and Rs. 5 coins is 20.
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