Question

A chemist has a container of 12% peroxide solution and a container of 20% peroxide solution. She needs to mix the two solutions to create 100 mL of a 14% solution. If x represents the amount of 12% peroxide solution and y represents the amount of 20% peroxide solution she needs, which matrix equation can determine the amount of each solution she needs to make the 14% solution?

Answer 1

Since the total amount of the mixture is 100mL, thus, the sum of the amount of the 12% peroxide in the solution plu the sum of the 20% peroxide in the solution is 100mL.

Thus, 

$x+y=100$

Also, since the resulting concentration of the mixture is 14% = 0.14.

Thus, 

$0.12x+0.2y=0.14$

Therefore, the matrix equation that can be used to determine the amount of each solution needed is given by:

$\left[\begin{array}{cc}1&1\\0.12&0.2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}100\\0.14\end{array}\right]$

Answer 2

Answer:

$\begin{bmatrix}1&1\\0.12 &0.2\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}100\\0.14\end{bmatrix}$

Step-by-step explanation:

We are given that,

The amount of 12% peroxide solution = x and the amount of 20% peroxide solution = y.

Since, the total amount of the solution to be made is 100 ml. So, the equation is $x+y=100$

Also, the sum of the 12% solution and 20% of the solution is resulting in 14% solution. Then, the equation is $0.12x+0.2y=0.14$

Thus, the system of equations is given by,

$x+y=100\\\\0.12x+0.2y=0.14$

Converting the system of equations to matrix form $Ax=B$, we get,

$\begin{bmatrix}1&1\\0.12 &0.2\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}100\\0.14\end{bmatrix}$