Kevin and Randy Muise have a jar containing 72 ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is ​$12.80. How many of each type of coin do they​ have?

This is a system of equations problem. To start, set up the equation for the total amount of coins. You know there are 72, and only 2 types of coins. We can assign x as the variable for quarters and y as the variable for nickels. Knowing this, our first equation is
x+y=72
The next equation sets up the amount of money the coins add up to. The total is 12.80. The equation will model the amount of money contributed by quarters + the amount of money contributed by nickels
.25x + .05y = 12.80
Next just solve for one variable using the first equation and substitute it in
X=72-y, so .25(72-y)+.05y=12.80
18-.25y+.05y=12.80
5.2=.2y
Y=26
Then we put that back into our first equation and get x=46
46 quarters and 26 nickels. This can be checked by plugging into the second equation. .25(46)+.05(26)=12.80