Question

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

Answer 1

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.

Answer 2

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.