Let n = number of nickels and d = number of dimes. So the first part of your problem, "There are 30 coins in the jar" gives us the equation:
n + d = 30
The second part of the problem, "...the total value of the coins is $2.30", gives us the equation:
0.05n + 0.10d = 2.30
So, our system of equation is:
n+d=30
0.05n+0.10d=2.30
If we multiply everything in the first equation by 10 and everything in the second equation by -100, we would have:
10n+10d=300
-5n-10d=- 230
If we now combine the equation by adding like terms together, we get
5n = 70
which gives us n = 12
Since there are a total of 30 coins and 12 of them are nickels, that means there are 18 dimes. So our solution is:
n=12
d=18
