Question

In the lab, Heather has two solutions that contain alcohol and is mixing them with each other. She uses 4 times as much Solution A as Solution B. Solution A is

15% alcohol and Solution B is 12% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 216 milliliters of pure alcohol?

Answer 1

1200 ml

Step-by-step explanation:

Let x be the quantity ( in ml ) of b solution,

∵ solution a is 100 milliliters less of than solution b.

So, the quantity of solution a = 100 - x,

Now, solution a has 13% alcohol,

∴ Alcohol in solution a = 13% of (100-x) = = 0.13(x-100),

While solution b has 17% alcohol,

∴ Alcohol in solution b = 17% of x = 0.17x,

So, the quantity of alcohol in the mixture of a and b = 0.13(x-100) + 0.17x

= 0.13x - 13 + 0.17x

= 0.30x - 13

According to the question,

Total quantity of alcohol in the mixture = 347 ml,

⇒ 0.30x - 13 = 347

⇒ 0.30x = 347 + 13

⇒ 0.30x = 360

⇒ x = = 1200

Hence, the quantity of solution b is 1200 ml.