How do I set this up to solve?
In 2004, the Diabetic Express charged $27.06 for a vial of Humulin insulin and $34.39 for a vial of Nevolin Velosulin insulin. If a total of $1565.57 was collected for 50 vials of Insulin, how many vials of each type were sold?
Solve this pair of equations for x and y.
x + y = 50
27.06 x + 34.39 y = 1565.57
Try substiting 50-x for y in the second equation.
To solve this problem, you need to set up a system of equations based on the given information. Let's assume the number of vials of Humulin insulin is represented by 'x', and the number of vials of Nevolin Velosulin insulin is represented by 'y'.
According to the problem, the price of a vial of Humulin insulin is $27.06, and the price of a vial of Nevolin Velosulin insulin is $34.39. The total amount collected for 50 vials of insulin is $1565.57.
Now, we can set up two equations:
1) The first equation represents the total cost of Humulin insulin and Nevolin Velosulin insulin:
27.06x + 34.39y = 1565.57
2) The second equation represents the total number of vials sold:
x + y = 50
To solve this system of equations, you can use various methods such as substitution, elimination, or matrices. Let's use the substitution method here:
From the second equation, we have x = 50 - y. Substitute this value of x into the first equation:
27.06(50 - y) + 34.39y = 1565.57
Now, simplify and solve for y:
1353 - 27.06y + 34.39y = 1565.57
7.33y = 212.57
y ≈ 29
Now, substitute the value of y back into the second equation to find x:
x + 29 = 50
x = 50 - 29
x = 21
Therefore, 21 vials of Humulin insulin and 29 vials of Nevolin Velosulin insulin were sold.