A chemistry student needs to make 60 liters of a 30% alcohol solution. He has a 20% alcohol solution and a 40% alcohol solution in the lab. How many liters of each strength does he need to mix together
*The system of equations I did was: a+b=60 & .2a+.4b=18. I may be wrong but i seriously need help
then a = (60-b)
.2(60-b) + .4 b = 18
12 - .2 b + .4 b = 18
.2 b = 6
b = 30
a = 30
You are seriously right in your equations.
You're on the right track! To solve this problem, you can set up a system of equations based on the given information.
Let's use the variables "a" and "b" to represent the volumes of the 20% and 40% alcohol solutions, respectively, that the student needs to mix.
The total volume of the final solution is 60 liters, so we know that a + b = 60.
The concentration of alcohol in the 20% solution is 20%, which means there are 0.20 liters of alcohol in every liter of solution. Similarly, the concentration of alcohol in the 40% solution is 40%, or 0.40 liters of alcohol per liter of solution.
The student needs to make a 30% alcohol solution. This means that the total volume of alcohol in the final solution should be 0.30 multiplied by 60 liters (since the total volume is 60). So, the total volume of alcohol is 0.30 * 60 = 18 liters.
Now we can set up the second equation based on the total volume of alcohol:
0.20a + 0.40b = 18
So, altogether, we have the following system of equations:
a + b = 60
0.20a + 0.40b = 18
To solve this system of equations, you can use the method of substitution or elimination. Let's use the method of substitution:
From the first equation, we can isolate a by subtracting b from both sides:
a = 60 - b
Now, substitute this expression for a in the second equation:
0.20(60 - b) + 0.40b = 18
Simplify and solve for b:
12 - 0.20b + 0.40b = 18
0.20b = 18 - 12
0.20b = 6
Divide both sides by 0.20:
b = 6 / 0.20
b = 30
Now, substitute this value for b into the first equation to solve for a:
a + 30 = 60
a = 60 - 30
a = 30
Therefore, the student needs to mix 30 liters of the 20% alcohol solution and 30 liters of the 40% alcohol solution to obtain 60 liters of a 30% alcohol solution.