Question

A motel clerk counts his $1 and $10 bills at the end of the day. He finds that he has a total of 53 bills having a combined monetary value of $215. Find the number of bills of each denomination that he has

Answer 1

Let the number $1 and $10 bills with the motel clerk be x and y respectively. Since he has a total of 53 bills, hence x+y=53….(1). Also, since the combined monetary value of the bills is $215, hence x*1 + y*10 = 215 or, x+10y = 215 …(2).

Now, on subtracting the 1^st equation from the3 2^nd equation, we get x+10y -x-y = 215-53 or, 9y = 162 so that y = 162/9 = 18. On substituting y = 18 in the 1^st equation, we get x+18 = 53 so that x = 53-18 = 35.

Thus, the number $1 and $10 bills with the motel clerk are 35 and 18 respectively.