Answer:
Step-by-step explanation:
Given that a solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol.
Let x gallons of 12% alcohol be mixed with y gallons of 4% alcohol.
Total gallons[tex]= x+y = 20[/tex]
Alcohol content in the total mixture [tex]= 0.12x+0.04y =9% of x+y[/tex]
[tex]0.12x+0.4y=0.09(20)\\12x+4y = 180[/tex]
b) Two equations are
[tex]x+y = 20\\12x+4y = 180[/tex]
c) This is of the form Ax = B
where A =[tex]\left[\begin{array}{ccc}1&1\\12&4\end{array}\right][/tex]
Inverse is [tex]\frac{1}{4-12} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\=\frac{-1}{8} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\[/tex]
Solution set is A inverse *B
= [tex]x \ 12.5\\y \ 7.5[/tex]
