A cash register contains only ten dollar and fifty dollar bills. It contains three times as many ten dollar bills as fifty dollar bills and the total amount of money in the cash register is $2,080. How many ten dollar bills are in the cash register?
The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 79 cm22, what is the length of the diagonal?
Let's start by assigning variables to the unknowns in the problem.
Let:
x = number of fifty dollar bills
3x = number of ten dollar bills
We are given two pieces of information.
First, the total number of dollars in the cash register is $2,080. Since each fifty dollar bill is worth $50 and each ten dollar bill is worth $10, we can write an equation for the total amount of money:
50x + 10(3x) = 2080
Simplifying the equation:
50x + 30x = 2080
80x = 2080
x = 2080 / 80
x = 26
Now that we know x = 26, we can substitute it back into the expression for the number of ten dollar bills:
3x = 3 * 26 = 78
Therefore, there are 78 ten dollar bills in the cash register.
To find the number of ten dollar bills in the cash register, we need to set up equations based on the given information.
Let's assume the number of fifty dollar bills is x.
According to the problem, there are three times as many ten dollar bills as fifty dollar bills, so the number of ten dollar bills would be 3x.
The value of each fifty dollar bill is $50 and the value of each ten dollar bill is $10.
Now let's set up the equation based on the total value of the money in the cash register:
50x + 10(3x) = 2080
Simplify the equation:
50x + 30x = 2080
Combine like terms:
80x = 2080
Now, we can solve for x by dividing both sides of the equation by 80:
x = 2080 / 80
x = 26
So, there are 26 fifty dollar bills in the cash register.
To find the number of ten dollar bills, we can substitute this value back into our equation for the number of ten dollar bills:
3x = 3 * 26 = 78
Therefore, there are 78 ten dollar bills in the cash register.
t = 3 f
10 t + 50 f = 2080
10 t + 50 (t/3) = 2080
30 t + 50 t = 6240
80 t = 6240
t = 78 tens