A 10% acid solution is to be mixed with a 50% solution to get 200 liters of a 20% solution. How many liters of each solution should be used?
.1x + .5(200-x) = .2(200)
.1x + 100 -.5x = 40
-.4x + 100 = 40
-.4x + 100-100 = 40-100
-.4x = -60
x = 150
10% at 150 and 50% at 50
Thank you Kuai!
Let's assume x liters of the 10% acid solution is used, and therefore (200 - x) liters of the 50% solution is used.
The amount of acid in the 10% solution is 0.10x liters (10% is written as 0.10 in decimal form), and the amount of acid in the 50% solution is 0.50(200 - x) liters.
To find the amount of acid in the resulting 20% solution, we set up the equation:
0.10x + 0.50(200 - x) = 0.20(200)
Let's solve the equation step-by-step:
0.10x + (0.50)(200 - x) = 0.20(200)
0.10x + 100 - 0.50x = 40
-0.40x + 100 = 40
-0.40x = 40 - 100
-0.40x = -60
Now, let's solve for x by dividing both sides of the equation by -0.40:
x = (-60) / (-0.40)
x = 150
So, 150 liters of the 10% acid solution should be used.
To find the amount of the 50% solution, we use the equation:
200 - x = 200 - 150 = 50
Therefore, 50 liters of the 50% solution should be used.
To summarize, to obtain 200 liters of a 20% solution, you should mix 150 liters of the 10% solution with 50 liters of the 50% solution.
To solve this problem, we can use the concept of mixtures.
Let's assume that x liters of the 10% acid solution is used. Therefore, the remaining quantity of the 200 liters solution will be (200 - x) liters of the 50% acid solution.
Now, let's calculate the amount of acid in each solution:
Amount of acid in the 10% solution = 0.10x liters
Amount of acid in the 50% solution = 0.50(200 - x) liters
Since we want to obtain a 20% solution, the amount of acid in the final solution will be:
Amount of acid in the final solution = 0.20(200) liters = 40 liters
Now, we can set up an equation based on the amount of acid:
0.10x + 0.50(200 - x) = 40
Simplifying the equation:
0.10x + 100 - 0.50x = 40
-0.40x + 100 = 40
-0.40x = -60
x = -60 / -0.40
x = 150
Therefore, 150 liters of the 10% acid solution should be used and the remaining quantity, (200 - 150) = 50 liters, should be the 50% acid solution.