How much 10% solution should she add? (answer in ml)

Question

A pharmacist wishes to mix a solution that is 8% Minoxidil. She has on hand 80ml of a 3% solution and wishes to add some 10% solution to obtain the desired 8% solution. How much 10% solution should she add?

Answer 1

Let x be the amount of the 10% solution to add to the 80ml of 3% solution to make 8% of the total solution.

0.03(80) + 0.10x = 0.08(x+80)

2.4 + 0.1x = 0.08x+6.4

0.02x = 4

x= 200 ml

Answer 2

80(.03) + .10x = .08(80+x)

2.4 -6.4 = .08x -.1x

4= .02x

x = 4/.02 = 200 mL of 10%

mixed with 80 mL 3%

yields 280 mL 8%

10-8=2

8-3 =5

5/2 = 2 1/2 times as much 10% as 3%

x/80 = 2.5

x = 200 mL 10%