Question 1044620
How many quarts of pure antifreeze must be added to 5 quarts 
of a 10% antifreeze solution to obtain a 40% antifreeze solution?
<pre><b>
Here's another way to think of it:

The 5 quarts of 10% antifreeze contains (5)(0.10) = 0.5 quart of pure 
antifreeze, (and the rest of the 5 quarts is 4.5 quarts of water, 
which we aren't concerned with).

We are adding X quarts of pure antifreeze to the 0.5 quarts of pure 
antifreeze (and water).  So after pouring them together, 
there will be X+0.5 quarts of pure antifreeze in the mixture.  And 
that will make 5+X quarts of liquid.

The equation is 

{{{matrix(1,12,number, of, quarts,of,PURE,ANTIFREEZE,only, contained, in, the, final, mixture)/matrix(1,9,number, of, quarts,of,LIQUID, in, the, final, mixture)}}}{{{""=""}}}{{{"40%"=40/100=0.4}}}

            {{{(X+0.5)/(5+X)}}}{{{""=""}}}{{{0.4}}}

Multiply both sides by (5+X)

            {{{X+0.5}}}{{{""=""}}}{{{0.4(5+X)}}}

            {{{X+0.5}}}{{{""=""}}}{{{2.0+0.4X)}}}

Multiply through by 10 to clear the decimals.  

            {{{10X+5}}}{{{""=""}}}{{{20+4X)}}}

            {{{6X}}}{{{""=""}}}{{{15}}}

            {{{X}}}{{{""=""}}}{{{15/6}}}

            {{{X}}}{{{""=""}}}{{{5/2}}}

            {{{X}}}{{{""=""}}}{{{matrix(1,2,2.5,quarts)}}}

Edwin</pre></b>