In 2009, a diabetic express company charged $38.85 for a vial of type A insulin and $30.49 for a vial of type B insulin. If a total of $2004.96 was collected for
60 vials of insulin, how many vials of each type were sold?
Let Type A = x
Let Type B = (60 - x)
Therefore Type A Type B = Totals
$38.85x $30.49(60 - x) = 2004.96
$38.85x $1829.4 - $30.49x = 2004.96
$38.85x - $30.49x =$ 2004.96 - $1829.4
$8.36x/8.36 = $175.56/8.36
X = 21
Type A = 21
Type B = (60 - x) = 60 - 21 = 39
In 2009, a diabetic express company charged $37.75 for a vial of type A insulin and $
30.49 for a vial of type B insulin. If a total of $1684.22 was collected for 50 vials of insulin, how many vials of each type were sold?
Let's assume the number of vials of type A insulin is represented by 'x', and the number of vials of type B insulin is represented by 'y'.
According to the given information, we can set up two equations:
1. The total cost equation:
38.85x + 30.49y = 2004.96
2. The total number of vials equation:
x + y = 60
To solve this system of equations, we can use the method of substitution.
First, we solve equation 2 for x:
x = 60 - y
Now we substitute this value of x into equation 1:
38.85(60 - y) + 30.49y = 2004.96
Expanding the equation:
2331 - 38.85y + 30.49y = 2004.96
Combining like terms:
8.64y = 326.04
Dividing both sides by 8.64:
y = 37.75
Now substitute this value of y back into equation 2 to find x:
x + 37.75 = 60
x = 60 - 37.75
x = 22.25
Therefore, 22.25 vials of type A insulin and 37.75 vials of type B insulin were sold. Note that you cannot have a fraction of a vial, so it is likely that the number of vials sold was rounded to the nearest whole number.
To solve this problem, let's assign variables to represent the number of vials of type A and type B insulin sold. Let's say x represents the number of vials of type A insulin and y represents the number of vials of type B insulin.
We are given the following information:
1. The price of a vial of type A insulin is $38.85
2. The price of a vial of type B insulin is $30.49
3. The total amount collected for 60 vials of insulin is $2004.96
From the given information, we can create two equations:
1. x + y = 60 (Equation 1: Total number of vials sold)
2. 38.85x + 30.49y = 2004.96 (Equation 2: Total amount collected)
We can now solve this system of equations to find the values of x and y.
To solve the system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
From Equation 1, we can express x in terms of y:
x = 60 - y
Substituting x = 60 - y into Equation 2, we get:
38.85(60 - y) + 30.49y = 2004.96
Now, we can simplify and solve for y:
2327 - 38.85y + 30.49y = 2004.96
-8.36y = 2004.96 - 2327
-8.36y = -322.04
Dividing both sides by -8.36, we get:
y = 38.48
Now, substitute this value of y back into Equation 1 to find x:
x + 38.48 = 60
x = 60 - 38.48
x = 21.52
So, the number of vials of type A insulin sold is approximately 21.52, and the number of vials of type B insulin sold is approximately 38.48. Since we cannot have fractional vials, we can assume that 21 vials of type A insulin and 38 vials of type B insulin were sold.