Can somebody please help me with this?

Mathematics

1 answer:

Natali5045456 [20]3 years ago

6 0

I would say C, but it also might be d

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A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing

stepan [7]

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 $= x+y = 20$

Alcohol content in the total mixture $= 0.12x+0.04y =9% of x+y$

$0.12x+0.4y=0.09(20)\\12x+4y = 180$

b) Two equations are

$x+y = 20\\12x+4y = 180$

c) This is of the form Ax = B

where A = $\left[\begin{array}{ccc}1&1\\12&4\end{array}\right]$

Inverse is $\frac{1}{4-12} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\=\frac{-1}{8} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\$