Question

Diane has $1.85 in dimes and nickels. she has a total of 23 coins. how many of each kind does she have? how many nickles? how many dimes?

Answer 1

The two equations for the set up are:
x+y=23 where x is the number of dimes and y is the number of nickles
10x+5y=185 
Now you solve by elimination and substitution.
Multiply your first equation by -5 and add the two equations together
-5x-5y=-115
+10x+5y=185
-------------------
5x=70
x=14

Substitute that into your original equation:
14+y=23
y=9

So you have 14 dimes and 9 nickles.

Hope this helps