Thirty liters of a 40% acid solution is obtained by mixing a 28% solution with a 43% solution.How much of each solution is required to obtain the specified concentration of the final mixture? Use this system of linear equations there x and y represents the amounts of the 28% solution and 43% solution. $$\left\{ \begin{array} { l }
x + y = 30 \
0.28 x + 0.43 y = 12
\end{array} \right.$$
A)28% solution: 6 L;43% solution: 24 L
B)43% solution: 6 L;28% solution: 24 L
C)28% solution: 40 L;43% solution: 24 L
D)43% solution: 40 L;28% solution: 24 L
E)43% solution: 7 L;28% solution: 24 L

Question

Thirty​ liters of a 40% acid solution is obtained by mixing a 28% solution with a 43% solution.How much of each solution is required to obtain the specified concentration of the final mixture? Use this system of linear equations there x and y represents the amounts of the 28% solution and 43% solution. ​​ $$\left\{ \begin{array} { l } 
x + y = 30 \
0.28 x + 0.43 y = 12
\end{array} \right.$$ ​
A)​28% solution: 6 L;43% solution: 24 L
B)43% solution: 6 L;28% solution: 24 L​
C)​28% solution: 40 L;43% solution: 24 L
D)​43% solution: 40 L;28% solution: 24 L
E)​43% solution: 7 L;28% solution: 24 L

Quizplus · Accepted Answer

The system of equations correctly represents the problem, and solving it gives the amounts of each solution needed. The second equation should correctly represent the total amount of acid in the final solution, which is $30 \times 0.4 = 12$ liters, not directly equal to 12 as stated. Solving the system yields 6 liters of the 28% solution and 24 liters of the 43% solution.

Thirty​ Liters of a 40% Acid Solution Is Obtained by Mixing

Thirty Liters of a 40% Acid Solution Is Obtained by Mixing