how much of a 25% solution should to be added to 35% solution to get 40 liters of 28% solution
Let the ratio of 35% and 25% solutions be x:(1-x)
To get a 28% solution,
35*x + 25*(1-x) = 28
35x-25x = 28 - 25
x = 3/10 (35%)
(1-x) = 1-3/10 = 7/10 (25%)
35% solution required for 40 litres of mixture
= 40*x = 12 litres
25% solution required for 40 l. of mixture
= 40(1-x) = 40 * 7/10 = 28 litres.
Check: 28+12=40 litres.
or
.25x + .35(40-x) = .28(40)
multiply by 100 and solve
x = 28
To determine how much of a 25% solution should be added to a 35% solution to get 40 liters of a 28% solution, you can follow these steps:
1. Let's assume x liters of the 25% solution should be added.
2. Therefore, the remaining amount from the total 40 liters will be (40 - x) liters of the 35% solution.
3. Now, we can calculate the amount of pure substance (in this case, it can be considered as alcohol) in each solution.
4. For the 25% solution, the amount of pure substance is (0.25 * x) liters.
5. For the 35% solution, the amount of pure substance is (0.35 * (40 - x)) liters.
6. The total amount of pure substance in the final mixture should be (0.28 * 40) liters.
7. Now, equate the amount of pure substance from the 25% and 35% solutions to the total amount of pure substance in the final mixture:
(0.25 * x) + (0.35 * (40 - x)) = 0.28 * 40
8. Simplify and solve this equation to find the value of x:
0.25x + 14 - 0.35x = 11.2
-0.1x = -2.8
x = 28
Therefore, you need to add 28 liters of the 25% solution to 12 liters of the 35% solution to obtain 40 liters of a 28% solution.