Algebra 2 system of equations word problem

Question

a pharmacist needs to prepare 15 milliliters of special eye drops for a glaucoma patient. The concentration of the active ingredient in the eye-drop solution must be 2%. The pharmacist only has in his stock these eye drops with 10% concentration and 1% concentration. Can the pharmacist fill the order? How?

Answer 1

Hi Weeer,

 

Let's begin by writing expressions for the ingredient concentration amounts of each solution:

    Solution #1 (10% solution) = (0.10)(x) ml.

    Solution #2 (1% solution) = (0.01)(15 - x) ml.

    Solution #3 (2% solution) = (0.02)(15) ml.

 

Next, let's write an equation to express the mixing of Solutions #1 & #2 to make up Solution #3 and then solve the equation for our two unknowns, (x) and

(15 - x):

    (0.10)(x) + (0.01)(15 - x) = (0.02)(15)

    0.10x + 0.15 - 0.01x = 0.30

    0.10x - 0.01x = 0.30 - 0.15

    0.09x = 0.15

    x = 0.15/0.09

    x = 5/3 ml. of Solution #1

     x = 1 and 2/3 ml. of Solution #1

    15 - x = 15 - 5/3

    15 - x = 45/3 - 5/3

    15 - x = 40/3 ml. of Solution #2

    15 - x = 13 and 1/3 ml. of Solution #2

 

We can verify our answers for each volume of solution needed by adding their concentrations amounts to together to see if they equal the desired concentration amount:

   (0.10)(1 and 2/3) + (0.01)(13 and 1/3) = (0.02)(15)

   (1/10)(5/3) + (1/100)(40/3) = 30/100

   5/30 + 40/300 = 30/100

   5/30 + 4/30 = 3/10

   9/30 = 3/10

   3/10 =3/10 

 

Since the sum of the input concentration amounts is equal the output concentration amount, we are confident that our input solution volumes are correct.

 

Given that there are 15 ml. of each solution in stock with which to make up the 15 ml. of the desired solution, we can conclude there is enough of each solution in stock to make up the desired solution.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan. 

Answer 2

Make sense