Kevin and randy muise have a jar containing 74 coins, all of which are either quarters or nickels. the total value of the coins in the jar is $12.90. how many of each type of coin do they have?

1 quarter is  1/4 of a dollar, that is   $0.25

1 nickel is $ 0.05

Let there be q quarters and n nickels. Thus the total value in the jar is: 
                                             $0.25q+$0.05n

The jar contains 74 coins, this means that :

i) q+n=74, so writing n in terms of q we have n=74-q

thus we have q quarters and 74-q nickels.

the total value of the coins in the jar is $12.90, 

so

12.90=0.25q+0.05n   substitute n with 74-q

12.90=0.25q+0.05(74-q)

12.90=0.25q+3.7-0.05q

12.90-3.7=0.25q-0.05q

9.2=0.2q

q=9.2/0.2=46

Thus n=74-q=74-46=28

28 nickels, 46 quarters

The variables should add up to equal 1