A chemist mixed a 70% alcohol solution with a 30% alcohol solution to make a 45% alcohol solution. How many liters of each were used to make 120 L of a 45% solution?

Question

I tried solving this with elimination method and made two separate equations. For instance,

x+y = 120(.45)
.70x+.30y=.45

This was the set up I came up with. But once I tried solving it I got an answer that I knew couldn't be right.

Answer 1

x = 70% alcohol solution

y = 30% alcohol solution

120 L of a 45% solution have :

120 * 0.45 = 54 L alcohol

Now you must solve system :

0.7 x + 0.3 y = 54

x + y = 120

The solutions are :

x = 45 L , y = 75 L

Proof :

0.7 * 45 + 0.3 * 75 = 31.5 + 22.5 = 54 L

x + y = 45 + 75 = 120 L