word problems in algebra

Question

A pharmacist is to prepare 15 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 4% active ingredient, but the pharmacist only has 10% solution and 1% solution in stock. How much of each type of solution should be used to fill the prescription?

1% solution ml

10% solution ml

Answer 1

10T + F = 8(15)

T+F = 15

F=15-T

10T + 15-T = 120

9T = 105

T = 105/9 = 11 2/3 milileters of the 10%

F = 15-11 2/3 = 3 1/3 mililters of the 1%

You know 8 is closer to 10 than to 1.

So there should be far more of the 10% than the 1%

8 is 2 away from 10

8 is 7 away from 1

8 is 7/9 of the the difference of 10 and 1

7/9 of 15 = 7/9 x 15 = 7/3 x 5 = 35/3 = 11 2/3 for 10% solution

2/9 of 15 = 2/9 x 15 = 2/3 x 5 = 10/3 = 3 1/3 for the 1% solution