In 2009, a diabetic express company charged $39.95 for a vial of type A insulin and $30.34 for a vial of type B insulin. If a total of $2022.21 was collected for 60 vials of insulin, how many vials of each type were sold?
If there are x vials of A, then then the rest (60-x) are of B. So, adding up the costs, we have
39.95x + 30.34(60-x) = 2022.21
Now just solve for x and then figure 60-x.
54534r4er
To solve this problem, we can set up a system of linear equations and use the method of substitution to find the solution.
Let's assume x represents the number of vials of type A insulin and y represents the number of vials of type B insulin.
Based on the given information, we can write the following two equations:
1) Cost of type A insulin: 39.95x
2) Cost of type B insulin: 30.34y
The sum of these costs should be equal to the total collected amount of $2022.21:
39.95x + 30.34y = 2022.21 --(Equation 1)
We also know that a total of 60 vials were sold, so we can set up another equation:
x + y = 60 --(Equation 2)
Now, we can solve this system of equations using substitution.
First, let's solve Equation 2 for x:
x = 60 - y
Now substitute this value of x into Equation 1:
39.95(60 - y) + 30.34y = 2022.21
Distribute the multiplication:
2397 - 39.95y + 30.34y = 2022.21
Combine like terms:
2397 - 9.61y = 2022.21
Subtract 2397 from both sides:
-9.61y = -374.79
Divide by -9.61:
y = 39.03
Now, substitute this value of y back into Equation 2 to find the value of x:
x + 39.03 = 60
x = 60 - 39.03
x = 20.97
So, there were approximately 21 vials of type A insulin and 39 vials of type B insulin sold.