Question

Sandra needs to make 500 L hand sanitizer with 75% alcoholic solution. He has only two of the alcoholic solutions available, a 65% solution and a 90% solution. How many litres of each alcoholic solution should he mix?

Answer 1

If Sandra mixes x L of 65% solution with y L of 90% solution, then the resulting mixture has a total volume of

x + y = 500

litres, and it contains

0.65x + 0.90y = 0.75 (500) = 375

litres of alcohol.

Solve the first equation for y :

y = 500 - x

Substitute this into the second equation and solve for x :

0.65x + 0.90 (500 - x) = 375

0.65x + 450 - 0.90x = 375

75 = 0.25x

x = 300

Solve for y :

y = 500 - 300

y = 200

So, Sandra should mix 300 L of 65% solution with 200 L of 90% solution.