How many milliliters of the 10% solution and of the 60% solution should be mixed?

Question

A chemist working on a flu vaccine needs to mix a 10% sodium-iodine solution with a 60% sodium-iodine solution to obtain 50 milliliters of a 30% sodium-iodine Solutions 

Answer 1

Set this up as a combination of the mixtures weighted by the percentages.

 

50 = milliliters of 30% mixture

x = milliliters of 10% solution

50 - x = milliliters of 60% solution

 

(10%)x + (60%)(50 - x) = (30%)(50)

 

10x + 60(50 - x) = 1500

 

-50x = -1500

 

x = 1500/50 milliliters = 30 milliliters

50 - x = (50 - 30) milliliters = 20 milliliters

 

You need 30 milliliters of the 10% mixture and 20 milliliters of the 60% mixture.

Answer 2

a + b = 50

10a + 60b = 30(50)

 

a = 50 - b

 

10(50 - b) + 60b = 1500

500 - 10b + 60b = 1500

50b = 1000

b = 20

 

a = 50 - 20 = 30