a bank teller has 52 $5 and $10 bills in her cash drawer. the value of the bills is $460. how many $5 bills are there?
add up the value of the bills:
5x + 10(52-x) = 460
5x + 520 - 10x = 460
5x = 60
x = 12
check:
5(12) + 10(40) = 60 + 400 = 460
Let's assign variables to represent the number of $5 and $10 bills.
Let's say the number of $5 bills is x, and the number of $10 bills is y.
We can set up two equations based on the given information:
1) x + y = 52 (since the total number of bills is 52)
2) 5x + 10y = 460 (since the total value of the bills is $460)
From equation 1, we can express y in terms of x as y = 52 - x.
Substituting this into equation 2, we get:
5x + 10(52 - x) = 460
5x + 520 - 10x = 460
-5x = -60
x = -60 / -5
x = 12
So, there are 12 $5 bills.
To solve this problem, we can use a system of equations. Let's represent the number of $5 bills as 'x' and the number of $10 bills as 'y'.
1. The first equation represents the total number of bills:
x + y = 52
2. The second equation represents the total value of the bills:
5x + 10y = 460
Now we have a system of equations:
x + y = 52
5x + 10y = 460
There are several methods to solve this system of equations, but let's use the substitution method:
From the first equation, we have:
x = 52 - y
Substitute this value for x in the second equation:
5(52 - y) + 10y = 460
Now, solve for y:
260 - 5y + 10y = 460
5y = 460 - 260
5y = 200
y = 200 / 5
y = 40
Therefore, there are 40 $10 bills.
Substitute this value of y in the first equation to find x:
x + 40 = 52
x = 52 - 40
x = 12
So, there are 12 $5 bills.
In conclusion, there are 12 $5 bills and 40 $10 bills.