When Ivan divides his coins into groups of 2 nickels and 1 quarter, worth $0.35, he find that he has $8.75/$0.35 = 25 such groups.
Ivan has 25 quarters and 50 nickels.
Let n denote the number of nickels.
and q denote the number of quarters.
1 nickel=0.05 dollar
and 1 quarter=0.25 dollar
Hence, we have:
0.05n+0.25q=8.75
( Since, Ivan has $8.75 in nickels and quarters in his desk drawer )
On multiplying both side of the equation by 100 we have:
5n+25q=875
on dividing both side of the equation by 5 we have:
n+5q=175-----------------(1)
Also, n=2q---------------(2)
( Since, the number of nickels is twice the number of quarters )
Hence, on putting equation (2) in equation (1) we have:
2q+5q=175
i.e.
7q=175
i.e. q=25
and on putting the value of q in equation (2) we have:
n=50
