Respuesta :
Answer: I need help on this one too xD
Step-by-step explanation:
Answer:
Correct answers:
30% solution: 40 liters, 60% solution: 20 liters
We are looking for how many liters of each solution are needed. Let x be the number of liters of the 30% solution, and let y be the number of liters of the 60% solution. He wants to get 60 liters of a 40% solution. A table will help us organize the data.
Type Number of units ⋅ Concentration = Amount
30% x 0.30 0.30x
60% y 0.60 0.60y
40% 60 0.40 0.40(60)
We multiply the number of liters times the concentration to get the total amount of alcohol in each solution. There are x(0.30)=0.3x liters of alcohol in x liters of the 30% solution, there are y(0.60)=0.6y liters of alcohol in y liters of the 60% solution, and he wants 60(0.40)=24 liters of alcohol in the 40% solution. We can translate this into a system of equations.
{x+y0.3x+0.6y=60=24
We will use the elimination method to solve this system. Multiplying the first equation by −0.3, we have
−0.3(x+y)0.3x+0.6y=−0.3(60)=24
Simplifying and adding leads to
−0.3x−0.3y0.3x+0.6y0.3y=−18=24=6
Dividing by 0.3, we have
y=20
Substituting this back into the first equation and solving for x, we have
x+yx+20x=60=60=40
We have found that he should mix x=40 liters of the 30% solution with y=20 liters of the 60% solution to get 60 liters of the desired 40% solution.
