Alcohol mixing solution

Question

You need a 85% alcohol solution. On hand, you have a 60 mL of a 75% alcohol mixture. How much pure alcohol will you need to add to obtain the desired solution?

Answer 1

60(.75) + (1.00)x = .85(60+x)

45 + x = 51 + .85x

.15x = 6

x = 6/.15 = 600/15 = 40 mL of pure 100% alcohol

mixed with 60 mL of 75% yields a mixture of 100 mL of 85% alcohol

75 is within 10 of 85

100 is within 15 of 85

you need 15/10 = 3/2 times as much 75% as pure alcohol

60 mL = (3/2)40 mL

Answer 2

Let y = amount of pure alcohol needed

Note that concentration of pure alcohol = 100% (so 1/1)

Note that we start with 60 mL of a 75% alcohol mixture and we need an 85% alcohol mixture

60 (0.75) + y (1) = 0.85 (y + 60)

45 + y = 0.85y + 51

So y - 0.85y = 6 -> 0.15y = 6

So y = 6/0.15 = 40 mL of alcohol