a motel clerk counts his 1$ and 10$ bills at the end of a day. He finds that he has a total of 57 bills having a combined monetary value of 156$. Find the number of bills of each denominaton that he has
x = number of ones
y = number of tens
x+ y = 57
x + 10 y = 156
hope this helps
To find the number of bills of each denomination, let's start by setting up a system of equations.
Let's assume the motel clerk has x number of $1 bills and y number of $10 bills.
According to the problem, the motel clerk has a total of 57 bills. So, the first equation we can write is:
x + y = 57 ...........(1)
The combined monetary value of the bills is $156. Since each $1 bill has a value of $1 and each $10 bill has a value of $10, we can write our second equation:
1x + 10y = 156 ...........(2)
To solve this system of equations, there are various methods you can use such as substitution, elimination, or graphing. Let's solve it using the substitution method.
From equation (1), we can express x in terms of y: x = 57 - y.
Substitute this x value into equation (2):
1(57 - y) + 10y = 156
57 - y + 10y = 156
9y = 156 - 57
9y = 99
y = 99/9
y = 11
Now, substitute the value of y back into equation (1) to find x:
x + 11 = 57
x = 57 - 11
x = 46
Therefore, the motel clerk has 46 $1 bills and 11 $10 bills.
So, the number of bills of each denomination is 46 $1 bills and 11 $10 bills.