Julia is a chemistry student. She is working on an experiment for which she needs 10 liters of a 20% salt solution. All she has in her lab are a 10% salt solution and a 40% salt solution. She decides to mix these to make her own 20% solution. How much of the 40% solution will she need to use? Round your answer to the nearest tenth of a liter.
.1 x + .4 y = .2(x+y)
but x = 10-y
.1(10-y) + .4 y = .2x + .2y
1 - .1 y + .4 y = .2 (10-y) + .2 y
(.4-.1 +.2-.2)y = 1
3 y = 10
y = 10/3
To determine how much of the 40% salt solution Julia should use, we need to set up an equation based on the given information.
Let's assume Julia needs to use "x" liters of the 40% salt solution.
Since she needs a total of 10 liters of the 20% salt solution, this means she will also use (10 - x) liters of the 10% salt solution.
To calculate the amount of salt in the final solution, we can sum up the salt in each component solution:
Amount of salt in the 40% solution = 40% * x liters = 0.4x liters of salt
Amount of salt in the 10% solution = 10% * (10 - x) liters = 0.1(10 - x) liters of salt
Since we want a final solution with 20% salt, the total amount of salt in the final solution will be:
Total amount of salt in the final solution = 20% * 10 liters = 0.2 * 10 = 2 liters of salt
Now, we can set up the equation:
0.4x + 0.1(10 - x) = 2
Simplifying the equation:
0.4x + 1 - 0.1x = 2
0.3x + 1 = 2
0.3x = 2 - 1
0.3x = 1
x = 1 / 0.3
x ≈ 3.3
Julia will need to use approximately 3.3 liters of the 40% salt solution to mix with the 10% salt solution to obtain a 20% salt solution.