A 5-quart solution of sulfuric acid and water is 60% acid. If a gallon of water is added, what percent of the resulting solution is acid?
a. 33 1/3%
b. 40%
c. 50%
D. none
Saw this question earlier on another site:
----------------------------------------------------------
A 5-quart solution of sulfuric acid and water is 60% acid.
If a gallon of water is added, what percent of the resulting solution is acid?
Let x = per cent when a gallon of water is added
Change 1 gallon to 4 quarts
The amt of acid remains the same
60(5) = x(5 + 4)
300 = 9x
x = 300/9
x = 33 1/3 percent
1 gal=4qt
5qt*0.6= 3 qt
there was 3 qt of acid in the original 5qt solution
5qt+1gal=5qt+4qt=9 quarts
3 quarts/9 quarts =1/3= 33 1/3%
0.6*5 = 3qts. acid and 2qts. water.
5+4 = 9qt. sol.
9-6 = 3qts acid.
3/9 * 100% = 33 1/3 % acid.
To find the percentage of acid in the resulting solution after adding a gallon of water, we can use a proportion.
Let's first determine the amount of acid in the original 5-quart solution. Since the solution is 60% acid, we can calculate it by multiplying the total volume (5 quarts) by the acid concentration (60%).
Amount of acid in original solution = 5 quarts x 60% = 3 quarts of acid
Next, let's determine the total volume of the resulting solution after adding a gallon of water. Since there are 4 quarts in a gallon, adding a gallon of water would increase the total volume to 5 quarts + 4 quarts = 9 quarts.
Now, we can calculate the percentage of acid in the resulting solution by setting up a proportion:
% of acid in resulting solution / 100% = amount of acid in resulting solution / total volume of resulting solution
% of acid in resulting solution / 100% = 3 quarts / 9 quarts
Cross multiply to solve for the percentage of acid in the resulting solution:
9 quarts * % of acid in resulting solution = 3 quarts * 100%
9 quarts * % of acid in resulting solution = 300%
Divide both sides of the equation by 9 quarts to isolate the percentage of acid:
% of acid in resulting solution = 300% / 9 quarts
Simplify:
% of acid in resulting solution = 33 1/3%
So, the resulting solution will be approximately 33 1/3% acid.
Therefore, the answer is (a) 33 1/3%.