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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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Solution 1. Two equations
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 = .
Thus you just found the volume of the 50% solution. It is gallons.
Then the volume of the 10% solution is t = = = gallons.
Solution 2. One equation.
This equation is
0.1t + 0.5*(10-t) = 0.25*10.
Simplify and solve for "t": t = , the same answer.