A motel clerk counts his​ $1 and​ $10 bills at the end of a day. He finds that he has a total of 70 bills having a combined monetary value of ​$250. Find the number of bills of each denomination that he has.

Answer 1

x = $1 bills

y = $10 bills

He finds that he has a total of 70 bills means:

x + y = 70

A combined monetary value of ​$250 means:

x ∙$1 + y ∙ $10 = $250

Now you must solve system:

x + y = 70

x + 10 y = 250
___________

In first equation subtract y to both sides

x = 70 - y

In second equation replace x with 70 - y

70 - y + 10 y = 250

70 + 9 y = 250

Subtract 70 to both sides

9 y = 180

y = 180 / 9

y = 20

x = 70 - y = 70 - 20

x = 50

50 $1 bills

20 $10 bills

Check result:

x + y = 20 + 50 = 70

50 ∙ $1 + 20 ∙ $10 = $50 + $200 = $250