Question 713286
That is an example of the general question:
How much of a higher concentration material must be mixed with some quantity of a lower concentration material to make a mixture of some intermediate value concentration?


L=35%, concentration of lower strength material
H=40%, concentration of higher strength matarial
T=38%, target concentration of mixture wanted
u= unknown, ounces of lower strength stuff to add
v=15 ounces, ounces of available higher strength stuff to be used.


The General Problem can be solved all in symbols:
{{{(Lu+Hv)/(u+v)=T}}}, we solve for u, the only unknown here.
{{{Lu+Hv=T(u+v)}}}
{{{Lu+Hv=Tu+Tv}}}
{{{Lu-Tu=-Hv+Tv}}}
{{{(L-T)u=(T-H)v}}}
{{{u=v(T-H)/(L-T)}}}, knowing that those differences are actually both negative we can do
{{{highlight(u=v(H-T)/(T-L))}}}


Now just substitute the given values to find u, the ounces of 35% alcohol.