A doctor orders 20 grams of a 52% solution of a certain medicine. The pharmacist has only bottles of 40% solution and bottles of 70% solution. How much of each must he use to obtain the 20 grams of the 52% solution?

Try, please, this:
1) Imagine, that pharmacist used 'x' gr. of 40% solution and 'y' of 70% solution.
Together (20 gr. of 52% sol.) it will be x+y=20.
2) From other side, the pharmacist combined 40x and 70y gramms, after obtaining together it is 52(x+y) gramms. In other words 40x+70y=52(x+y)
3) 
[tex] \left \{ {{x+y=20} \atop {40x+70y=52(x+y)}} \right. \ =\ \textgreater \ \ \left \{ {{y=8} \atop {x=12}} \right. [/tex]
Answer: 8 gr. of 70% solution and 12 gr. of 40%.