Georgia has only dimes and quarters in her bag. She has a total of 18 coins that are worth $3. How many more dimes than quarters does she have?

In order to solve this, you need a system of equations (you need #2# separate equations with the same two variables and find out what values make them both true).

To start, you can say, since there are #18# coins and they are only dimes and quarters #d+q=18#.

Next, since dimes are worth #10¢#, quarters are worth #25¢#, and the total amount of cash is #300¢# you can say #10d+25q=300#.

Now you have #d+q=18# and #10d+25q=300#. There are several ways to solve a system of equations like this one. My personal preference is elimination as that is typically fastest.

Multiply everything in the first equation by #-10# so we can cancel our #d# and solve for #q#.
#d+q=18 rArr -10d-10q=-180#

Then, add the second equation to the one we just made.
#-10d-10q=-180#
#+10d+25q=300#

#-10d# and #10d# cancel and we are left with
#15q=120#

Divide both sides by 15.
#q=8#

Now, go back to your first equation and plug in your #q# value.
#d+8=18#

Subtract #8# from both sides
#d=10#

The original question wants to know how many more dimes you have than quarters. (#d-q=?#)
#10-8=2#