Question 148698
1 Nickel =0.05  N= number of nickels
1 Dimes =0.1    D= number of dimes
1 quarter =0.25 Q=number of quarters

Mike has 19 coins then 

N+D+Q=19

total value of $2.35 then

 0.05N+0.1D+0.25Q=2.35

There are 2 more dimes than nickels then

 D=N+2

3 equations are:
N+D+Q=19
0.05N+0.1D+0.25Q=2.35
D=N+2

using the third eq in 1 and 2

N+N+2+Q=19
0.05N+0.1(N+2)+0.25Q=2.35

2N+Q=17  then Q=17-2N
0.15N+0.25Q=2.15

0.15N+0.25(17-2N)=2.15

0.15N+4.25-0.5N=2.15

-0.35N=-2.1

N=2.1/0.35=6

Q=17-2(6)=5

D=19-5-6=8

Answer:

N=6,D=8,Q=5