Alcohol mixture problem

Question

You need a 70% alcohol solution. On hand, you have a 150 mL of a 25% alcohol mixture. You also have 80% alcohol mixture. How much of the 80% mixture will you need to add to obtain the desired solution?

Answer 1

150(.25) + x(,8) = (150+x)(.7)

37.5 + .8x = 105 + .7x

.8x-7x = 105-37,5

.1x = 67.5

x = 675 mL of 80%

Answer 2

Hi Devon!

With these mixture-type problems, it helps to make a table like this:

Solution A | Solution B | Mixture

Amount

% Alcohol

Total Alcohol

Now we fill it in with what we know. If solution A is the one with 25% alcohol, we want to find the amount of Solution B to use. Let's call that amount b. Also, change the percents to decimals. Here's all the info we have so far:

Solution A | Solution B | Mixture

Amount 150 b

% Alcohol .25 .8 .7

Total Alcohol

Now we do a little math to fill in our table. Since we have 150 mL of A and b mL of b, our total mixture contains 150+b mL of fluid.

Since we have 150 mL of Solution A that's 25% alcohol, the total amount of alcohol in solution A is

150*.25=37.5 mL

Similarly, we have b mL of Solution B that's 80% alcohol, so the total amount in solution B is .8b

Filling those into the table:

Solution A | Solution B | Mixture

Amount 150 b 150+b

% Alcohol .25 .8 .7

Total Alcohol 37.5 .8b

Maybe you can see what to do now? The total alcohol in the mixture has to be the amount times the percent:

(150+b)*.7

Solution A | Solution B | Mixture

Amount 150 b 150+b

% Alcohol .25 .8 .7

Total Alcohol 37.5 . 8b (150+b)*.7

But, that also has to equal the sum of the total alcohol from Solutions A and B! So we finally have an equation:

37.5+.8b=(150+b)*.7

You probably already know how to solve that for b, but I'll write out the steps:

37.5+.8b=105+.7b I like to multiply through by 10 to clear the decimals

375+8b=1050+7b

8b-7b=1050-375

b=675 mL