in her chemistry class, Lauren must produce 300ml of an 80% acid solution. Her teacher gives her two concentrations of acid solution, a 50% and a 100%. determine how much of each concentration that she must use.
.5x + 1y = .8(300)
x + y = 300
x = 300 - y
.5(300-y) + 1y = 240
150 - .5y + 1y = 240
1/2y = 90
y = 180 ml
300-180 = x = 120ml
use 120ml 50%
use 180ml 100%
To find out how much of each concentration Lauren should use, we can set up a system of equations based on the given information.
Let x represent the volume (in ml) of the 50% acid solution that Lauren needs to use.
Similarly, let y represent the volume (in ml) of the 100% acid solution that Lauren needs to use.
According to the problem, the two concentrations of acid solution are 50% and 100%, and the desired total volume of the solution is 300 ml. Therefore, we can write the following equations:
Equation 1: x + y = 300 (total volume equation)
Equation 2: 0.50x + 1.00y = 0.80(300) (acid concentration equation)
Simplifying Equation 2, we have:
0.50x + y = 0.80(300)
0.50x + y = 240
Now, we can solve this system of equations using any method such as substitution or elimination. Let's use the elimination method to solve it.
Multiplying Equation 1 by -0.50 will allow us to eliminate the x variable when we add the two equations:
-0.50x - 0.50y = -150
0.50x + y = 240
Adding the two equations:
-0.50y + y = -150 + 240
0.50y = 90
y = 90 / 0.50
y = 180
Now that we have found the value of y, we can substitute it back into Equation 1 to find x:
x + 180 = 300
x = 300 - 180
x = 120
So, Lauren must use 120ml of the 50% acid solution and 180ml of the 100% acid solution to produce 300ml of an 80% acid solution.
To determine how much of each concentration Lauren needs to use, we can set up a system of equations based on the information given.
Let's assume Lauren needs to use x ml of the 50% acid solution and y ml of the 100% acid solution.
The first equation is based on the total volume of the acid solution:
x + y = 300 (Equation 1)
The second equation is based on the concentration of acid in the solution:
(0.5x + y) / 300 = 0.8 (Equation 2)
In Equation 2, we take the sum of the amount of acid in the 50% solution (0.5x) and the amount of acid in the 100% solution (y), then divide by the total volume (300 ml) to get the concentration of acid, which is 80% of the solution.
Now, we can solve the system of equations to find the values of x and y.
Solving Equation 1 for x, we get:
x = 300 - y
Substituting this value of x into Equation 2, we have:
(0.5(300 - y) + y) / 300 = 0.8
Simplifying the equation, we get:
150 - 0.5y + y = 240
Combining like terms, we have:
0.5y = 90
Dividing both sides by 0.5, we find:
y = 180
Substituting this value of y into Equation 1, we get:
x + 180 = 300
x = 120
Therefore, Lauren needs to use 120 ml of the 50% acid solution and 180 ml of the 100% acid solution to produce 300 ml of an 80% acid solution.