Suppose a 2% acid solution is mixed with a 3% acid solution. Find the percent of acid in each mixture.
-a mixture that contains an equal amount of 2% acid solution and 3% acid solution
-a mixture that contains 3 times more 2% acid solution than 3% acid solution
equal amounts: 2.5%
if 3% solution is x times the 2% solution, then if the resulting concentration is y%,
.02 + .03x = (1+x)*y
You can see that if x=1, y=.05/2 = .025 = 2.5%
If x = 3, .11 = 4y, so y = .11/4 = .0275 = 2.75%
Makes sense, since the new concentration is 3/4 of the way from 2% to 3%.
Good thing you reposted it. I misread the problem, and solved it for having 3 times as much 3% as 2%. See bobpursley's solution for the correct answer.
Having read my algebra carefully, though, you should have been able to do it right.
To find the percent of acid in a mixture, you need to calculate the weighted average of the percent of acid in each solution based on the amount of solution used.
For the first mixture, where an equal amount of 2% acid solution and 3% acid solution is used:
1. Calculate the weighted average:
Percent of acid in the mixture = (Percent of acid in 2% solution + Percent of acid in 3% solution) / 2
Let's substitute the given values:
Percent of acid in the mixture = (2% + 3%) / 2
Percent of acid in the mixture = 5% / 2 = 2.5%
So, in a mixture that contains an equal amount of 2% acid solution and 3% acid solution, the percent of acid in the mixture would be 2.5%.
For the second mixture, where there is three times more 2% acid solution than 3% acid solution:
1. Let's assume we have 'x' amount of 3% acid solution.
So, we have 3 * x amount of 2% acid solution in this mixture.
2. Calculate the total amount of acid by adding the amount of acid from each solution:
Total amount of acid = (2% * 3 * x) + (3% * x) = 6x% + 3x%
3. Calculate the total amount of solution:
Total amount of solution = x + 3x = 4x
4. Calculate the percent of acid in the mixture:
Percent of acid in the mixture = (Total amount of acid / Total amount of solution) * 100
Percent of acid in the mixture = ((6x% + 3x%) / 4x) * 100
Simplifying further:
Percent of acid in the mixture = (9x% / 4x) * 100
Percent of acid in the mixture = 2.25 * 100
So, in a mixture that contains three times more 2% acid solution than 3% acid solution, the percent of acid in the mixture would be 225%.