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 $=\ y\ =\ 80$
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