Question

An after-shave lotion contains 45% ethyl alcohol. How much water must be added to 8 fluid ounces of this lotion to reduce it to one which is 70% nonalcoholic?

Answer 1

$\boldsymbol{\mathbf{Answer}}$

\boldsymbol{\mathbf{4 ounces water we need to add.}}

$\boldsymbol{\mathbf{Step-by-step explanation}}$

An after shave lotion contains 45% of ethyl alcohol

i.e 100% - 45% = 65% nonalcoholic

As mentioned, we have 8 ounces of fluid and that contains 45% of ethyl alcohol.

${=\,8}\times{0.45}$

i.e $\boldsymbol{\mathbf{3.6 ounces alcohol.}}$

We need fluid which 70% nonalcoholic.

i.e 100 - 70 = 30% of alcohol.

Then there is already 3.6 ounces of alcohol in fluid.

As required, Let consider 3.6 ounce is 30% of alcohol.

70% must be other liquid.

That is equal to =

= $\boldsymbol{\mathbf{\frac{3.6}{0.3}\times{0.7}}}$

= 8.4 Ounces Of other liquid.

Then total ounces of the lotion is

= 3.6 + 8.4

= 12 ounces.

Water required to add is,

= 12 - 8

= $\boldsymbol{\mathbf{4 ounces}}$