Question 1056579
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A taxidermist has a container with a solution of 10% tanning chemical and a container with a solution of 50% tanning chemical. 
If the taxidermist wants to mix the solutions to get 10 gallons of the solution with 25% tanning chemical, 
how many gallons of each solution should be mixed?
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<U>Solution 1</U>. Two equations


<pre>
Let "t" be the volume of the 10% tanning chemical to mix (in gallons), and
let "f" be the volume of the 50% tanning chemical to mix (in gallons).

Then you have these two equations

   t +    f = 10,        (1)    for the total volume
0.1t + 0.5f = 0.25*10    (2)    for the pure chemical amount.

Multiply (2) by 10. You will get

   t +    f = 10,        (1')   ( still (1) )
   t +   5f = 2.5*10     (2') 

Now distract (1') from (2') (both sides). You will get

   5f - f = 25 - 10,

   4f = 15   --->  f = {{{15/4}}}.

Thus you just found the volume of the 50% solution. It is {{{15/4}}} gallons. 

Then the volume of the 10% solution is t = {{{10-15/4}}} = {{{(40-15)/4}}} = {{{25/4}}} gallons.
</pre>


<U>Solution 2</U>.  One equation.


<pre>
This equation is

0.1t + 0.5*(10-t) = 0.25*10.

Simplify and solve for "t":  t = {{{25/4}}}, the same answer.
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