Alewuya needs to mix a 20% acid solution with a 40% acid solution to create 100 millileters of a 24% solution. How many millileters of each solution must Alewuya use?
−4( 2x + y ) − ( 4x + y )
=4x+4y-4x-4y
-8x-3y
If there are x ml of 20% then the rest (100-x) is 40%.
So, add up the acid in the parts; it must equal the acid in the result:
.20x + .40(100-x) = .24*100
and that's liters, not leters.
When you get your answer, note that 24% is 1/5 of the way from 20 to 40, so 1/5 of the mixture must be the higher concentration.
To solve this problem, we can use the concept of percentages and the equation:
(amount of acid in the 20% solution) + (amount of acid in the 40% solution) = (amount of acid in the 24% solution)
Let's assume Alewuya needs to use x milliliters of the 20% acid solution and y milliliters of the 40% acid solution.
The amount of acid in the 20% solution is 20% of x, which can be written as 0.20x.
The amount of acid in the 40% solution is 40% of y, which can be written as 0.40y.
The amount of acid in the final 24% solution is 24% of 100 milliliters, which can be written as 0.24 * 100 = 24.
So now we have the equation:
0.20x + 0.40y = 24
We also know that the total volume of the two solutions must add up to 100 milliliters:
x + y = 100
Now we have a system of two equations that we can solve simultaneously to find the values of x and y.
One way to solve this is by substitution. Rearrange the second equation to solve for x:
x = 100 - y
Substitute this expression for x in the first equation:
0.20(100 - y) + 0.40y = 24
Now solve for y:
20 - 0.20y + 0.40y = 24
0.20y = 4
y = 20
Now substitute the value of y back into the second equation to solve for x:
x + 20 = 100
x = 80
Therefore, Alewuya needs to use 80 milliliters of the 20% acid solution and 20 milliliters of the 40% acid solution to create 100 milliliters of a 24% solution.