Hello Stephen

Welcome to Math Help Forum! Originally Posted by

**Stephen** could you please tell me how I set this up to solve? thanks

a veterinarian has two solutions that contain different concentrations of a certain medicine. One is 15% concentration and the other is 5 % concentration. How many cubic centimeters of each should the veterinarian mix to get 20 cc of a 6 % solution?

Suppose he uses $\displaystyle \displaystyle x$ cc of the first solution, and $\displaystyle \displaystyle y$ cc of the second. Then we can set up two simultaneous equations as follows:

The total volume must be 20 cc. Therefore

$\displaystyle \displaystyle x+y = ...$ ?

This is equation (1).

The quantity of the medicine in $\displaystyle \displaystyle x$ cc of the first solution is $\displaystyle \displaystyle \frac{15x}{100}$.

The quantity of the medicine in $\displaystyle \displaystyle y$ cc of the second solution is $\displaystyle \displaystyle \frac{5y}{100}$.

The total quantity of medicine in the mixture is therefore ... ?

This must be 6% of the total volume, $\displaystyle \displaystyle 20$ cc, which is $\displaystyle \displaystyle \frac{6\times 20}{100} = ...$ ?

The second equation is therefore

$\displaystyle \displaystyle \frac{15x}{100}+\frac{5y}{100}=...$ ?

This is equation (2).

Can you complete what I have started, and then solve the simultaneous equations to find $\displaystyle \displaystyle x$ and $\displaystyle \displaystyle y$?

Grandad