Finding x and y? Can someone help me with this problem. I came out with the answer of 7.8 ounces needed. I used x =15% solution and y = 35% solution. I just don't know for sure if I did it right. The problem is:
A 15% acid solution is to be mixed with a 35% acid solution to produce  12 ounces of a 22% acid solution. How much of the 15% acid solution is needed?
Let x = ____
Let y = ____
Thank you. 
 A: You were right' we need 7.8 ounces of 15% solution and 4.2 ounces of 35% solution to come up with a 12 ounces of 22% acid solution.
The main equation will be:
$.15x+.35(12-x)=12(.22)$ solving for $x$ we get 7.8.
Congrats.
A: This problem is expressed mathematically as
$$ 0.15x+0.35y=12(0.22) $$
$$ x+y=12 $$
This implies that
$$ y=12-x $$
So now we have
$$ 0.15x+0.35(12-x)=12(0.22) $$
$$ 0.15x+(12)0.35-0.35x=12(0.22) $$
$$ 0.15x+4.2-0.35x=2.64 $$
$$ 0.15x-0.35x=2.64 -4.2$$
$$ -0.2x=-1.56$$
$$ 0.2x=1.56$$
$$ x=\frac{1.56}{0.2}=7.8$$
So yes, your solution is correct.
A: Yes, $7.8$ is the correct answer.
Your problem can be modeled by a system of two equations:
$$\begin{cases}0.15x+0.35y=12\cdot0.22\\
x+y = 12
\end{cases}$$
To solve it, you can use any of the many techniques available. For example, multiplying the two sides of the second equation by $0.15$:
$$\begin{cases}0.15x+0.35y=12\cdot0.22\\
0.15x+0.15y = 12\cdot0.15
\end{cases} \stackrel{subtracting}{\implies}\begin{cases}y = 5\cdot12\cdot0.07\\
x + y = 12
\end{cases}\implies \begin{cases}y = 4.2\\
x = 7.8
\end{cases}$$
