A motel clerk counts his $1 and $10 bills at the end of the day. he finds that he has a total of 56 bills having a combined monetary value of $182. find the number of bills of each denomination that he has

We can write a system of equations:

1x + 10y = 182

x + y = 56

Where 'x' is the number of $1 bills, and 'y' is the number of $10 bills.

To find this we can solve using substitution.

Re-arrange the 2nd equation:

x + y = 56

Subtract 'y' to both sides:

x = - y + 56

Now we can plug in '-y + 56' for 'x' in the first equation.

1x + 10y = 182

1 (-y + 56) + 10y = 182

-y + 56 + 10y = 182

Subtract 56 to both sides:

-y + 10y = 126

Combine like terms:

9y = 126

Divide 9 to both sides:

y = 14

Now we can plug this into any of the two equations to find the 'x' value.

x + y = 56

x + 14 = 56

Subtract 14 to both sides:

x = 42

So our final answer is (42, 14).

This means that the motel clerk had 42 $1 bills, and 14 $10 bills.