Application of linear systems

Question

A motel clerk counts his $1 and $10 bills at the end of the day. He finds that he has a total of 60 bills having a combined monetary value of $150. Find the number of bills of each denomination that he has.

Answer 1

Let x = # of $1 bills and y = $10 then

x + y = 60 → x = 60 - y

x + 10y = 150

We can solve via substitution:

x + 10y = 150

(60 - y) + 10y = 150

60 + 9y = 150

9y = 90

y = 10

y = 10 and x = 60 - y , so x = 60 - 10 = 50

He has 50 $1 bills and 10 $10 bills.