I’m hotel clerk counts his one dollar bills and $10 bills at the end of the day he finds that he has a total of 59 bills having a combined monetary value of $185 find the number of bills and each denomination that he has

You can either do this in one variable or 2.

If you do it in two variables you have two equations, that will need to be solved : )
Let x represent the one dollar bills and y the 10$ bills
x + y = 59 bills.
Now we have to deal with the value of the money for equation 2.
1x + 10y = 185
Now you have many ways to solve for x and y : )
If you do "substitution" you could re-arrange equation 1 to isolate x or y...
x = 59 - y
then sub that into your second equation and solve for y : )
Then once you have y sub it back into one of the original equations and solve for x.

He has X $1 bills.

Y $10 bills.

Eq1: x + y = 59.
Eq2: x + 10y = 185.
Multiply Eq1 by -1 and add Eq1 and Eq2:
-x - y = -59
x + 10y = 185
Sum: 9y = 126,
Y = 14.
In Eq1, replace y with 14 and solve for x.

To find the number of bills and each denomination that the hotel clerk has, we can set up a system of equations based on the given information.

Let's represent the number of one dollar bills as 'x' and the number of $10 bills as 'y'.

From the problem statement, we have two pieces of information:

1. The total number of bills is 59: x + y = 59.
2. The combined monetary value is $185: 1x + 10y = 185.

Now we can solve this system of equations to find the values of 'x' and 'y'.

The first equation is already in the form that we need, so we don't need to do anything with it.

To simplify the second equation, we need to combine like terms:

x + 10y = 185.

Now we have a system of equations:

x + y = 59,
x + 10y = 185.

We can solve this system by using the method of substitution or elimination. Let's use the method of substitution:

Solve the first equation for x:
x = 59 - y.

Substitute this value in the second equation:
(59 - y) + 10y = 185.

Simplify the equation:
59 + 9y = 185.

Subtract 59 from both sides:
9y = 126.

Divide both sides by 9:
y = 14.

Now we have found the value of 'y' (number of $10 bills). Substituting this into the first equation, we can find the value of 'x' (number of one dollar bills):

x + 14 = 59,
x = 59 - 14,
x = 45.

Therefore, the hotel clerk has 45 one dollar bills and 14 $10 bills.