Alice is counting a cash register at the end of the night she has $1015 in $5 bills and $10 bills. if she has 138 bills all together, how many of each type does she have?

Let f and t be the number of fives and tens respectively...

f+t=138

f=138-t  and we are told that:

5f+10t=1015, using f from above in this equation gives you:

5(138-t)+10t=1015

690-5t+10t=1015

690+5t=1015

5t=325

t=65 and since f=138-t, 

f=73 so

Alice has 73 fives and 65 tens.