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 $1747.64 was collected for 50 vials of insulin, how many vials of each type were sold?
you are told that
A + B = 50
39.95A + 30.34B = 1747.64
Now go for it.
65
A+B=50
39.95A+30.34B=174.64
To find out how many vials of each type were sold, we can set up a system of equations based on the given information.
Let's assume x vials of type A insulin were sold and y vials of type B insulin were sold.
According to the given information, the price of a single vial of type A insulin is $39.95, and the price of a single vial of type B insulin is $30.34.
So, the first equation representing the total cost for type A insulin can be written as:
Cost of type A insulin = x * $39.95
Similarly, the total cost for type B insulin can be written as:
Cost of type B insulin = y * $30.34
The total cost for all the insulin sold is given as $1747.64. Therefore, we have our second equation:
Total cost = $1747.64
Now, we can combine these equations to form a system of equations:
x * $39.95 + y * $30.34 = $1747.64 (equation 1)
x + y = 50 (equation 2)
To solve this system of equations, we can use different methods such as substitution or elimination. Let's solve it using the elimination method:
Multiply equation 2 by $39.95 to make the coefficients of x in both equations equal:
($39.95)(x + y) = ($39.95)(50)
$39.95x + $39.95y = $1997.50 (equation 3)
Now, subtract equation 1 from equation 3 to eliminate x:
($39.95x + $39.95y) - ($39.95x + $30.34y) = $1997.50 - $1747.64
$9.61y = $249.86
Dividing both sides by $9.61, we get:
y = $249.86 / $9.61
y ≈ 26
Now, substitute the value of y in equation 2 to find the value of x:
x + 26 = 50
x = 50 - 26
x = 24
So, approximately 24 vials of type A insulin and 26 vials of type B insulin were sold.