A manager has $1170 made up of twenties and fifties. The total is 36 bills. How many fifty-dollar bills does the manager have?
Please show me how to set this problem up. I am confused.
You need to set up a system of equations. No one knows how many of each type of bill there is. Let t=twenties and f=fifties.
t+f=36
20t+50f=1170
-20(t+f=36)=-20t+-20f=-720
20t+50f=1170
30f=450 f=15
t+15=36
-15 -15
t=21
To determine the number of fifty-dollar bills the manager has, we need to set up a system of equations based on the given information. Let's denote the number of twenties as 'x' and the number of fifties as 'y'.
First, we know that the manager has a total of 36 bills, so we can set up the equation:
x + y = 36 -- Equation 1
Secondly, we know that the total amount of money the manager has is $1170. Since each twenty-dollar bill is worth $20 and each fifty-dollar bill is worth $50, we can formulate the equation for the total amount of money:
20x + 50y = 1170 -- Equation 2
Now we have a system of two equations with two variables. We can solve this system to find the solution.
To eliminate one of the variables, we can multiply Equation 1 by 20, which gives us:
20x + 20y = 720 -- Equation 3
By subtracting Equation 3 from Equation 2, we can eliminate 'x' and solve for 'y':
(20x + 50y) - (20x + 20y) = 1170 - 720
30y = 450
Dividing both sides of the equation by 30, we find:
y = 15
Therefore, the manager has 15 fifty-dollar bills.