# I have a total of rupees 300 in coins of denomination rupees 1, 2, 5 the number of rupees 2 coins is 3 times the number of rupees 5 coins. The total number of coins is 160. Find the number of coins of each denomination.

Given:

Total amount = Rs. 300

The number of rupees 2 coins is 3 times the number of rupees 5 coins.

To find: Here we have to find the number of coins of each denomination.

Solution:

Let the number of Rs 5 coins = $x$

So,

Number of Rs 2 coins = 3$x$

The number of Rs 1 coin = $y$

Total no. of coins = 160

$x\ +\ 3x\ +\ y\ =\ 160$

$4x\ +\ y = 160$

Given that, total amount is Rs. 300:

$5x\ +\ 2(3x)\ +\ y\ =\ 300$

$11x\ +\ y\ =\ 300$

By elimination method on subtracting both the equations

$4x\ +\ y\ -\ 11x\ -\ y\ =\ 160 -\ 300$

$-7x\ =\ -140$

$x\ =\ \frac{140}{7}$

$x\ =\ 20$

On putting the value of $x$ in $4x\ +\ y\ =\ 160$

$4(20)\ +\ y\ =\ 160$

$80\ +\ y\ =\ 160$

$y\ =\ 80$

Now,

Number of Rs 2 coins $=\ 3(x)\ =\ 3(20) =\ 60$

No. of Rs 5 coins $=\ x\ =\ 20$

No. of Rs 1 coins $=\ y\ =\ 80$