SOLUTION: a 10-quart container is filled with water.One quart of water is drained out and replaced with alcohol. After mixing a quart of the solution is drainec out and replaced with alcohol
Algebra.Com
Question 1145132: a 10-quart container is filled with water.One quart of water is drained out and replaced with alcohol. After mixing a quart of the solution is drainec out and replaced with alcohol. This process is continued until 5 quarts of alvohol have been put into the container. The solution in the container is then what percent of alcohol.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
At the start, the 10 quarts are 10 of water and 0 of alcohol.
(1) First time: When 1/10 (0.1) of the container is emptied, the amount of alcohol removed is (0.1)(0)=0, leaving 0; when 1 quart of alcohol is then added, the amount of alcohol is 0+1 = 1.
(2) Second time: When 1/10 (0.1) of the container is emptied, the amount of alcohol removed is (0.1)(1)=0.1, leaving 0.9; when 1 quart of alcohol is then added, the amount of alcohol is 0.9+1 = 1.9
(3) Third time: When 1/10 (0.1) of the container is emptied, the amount of alcohol removed is (0.1)(1.9)=0.19, leaving 1.71; when 1 quart of alcohol is then added, the amount of alcohol is 1.71+1 = 2.71
(4) Fourth time: When 1/10 (0.1) of the container is emptied, the amount of alcohol removed is (0.1)(2.71)=0.271, leaving 2.439; when 1 quart of alcohol is then added, the amount of alcohol is 2.439+1 = 3.439
(5) Fifth time: When 1/10 (0.1) of the container is emptied, the amount of alcohol removed is (0.1)(3.439)=0.3439, leaving 3.0951; when 1 quart of alcohol is then added, the amount of alcohol is 3.0951+1 = 4.0951
After the 5th time, the percentage of alcohol in the container is 4.0951/10 converted to a percentage, which is 40.951%.
ANSWER: 40.951%
And now that we have obtained the answer by that method, there is a much easier path....
Each time a quart of liquid is removed and replaced with a quart of alcohol, the fraction of water in the container gets multiplied by 0.9.
After 5 times, the fraction of the liquid in the container that is water is (0.9)^5 = 0.59049.
So after the 5th time the percentage of water in the container is 59.049%; so the percentage of alcohol is 100-59.049% = 40.951%.
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.
For the solution / solutions of TWIN problems, see the lesson
- Word problems on geometric progressions, Problems 1 and 2
in this site.
RELATED QUESTIONS
Please help me solve this problem...I dont know how to start solving this..
A 10-quart (answered by ankor@dixie-net.com)
A 12-quart cooling system is tested and found filled with a 60% antifreeze solution. The (answered by ankor@dixie-net.com)
A 12 quart cooling system is tested and found filled with a 60 percent antifreeze... (answered by lwsshak3)
a12-quart cooling system is tested and found filled with a 60% antifreeze solution. The... (answered by ad_alta)
A car radiator has a 16 quart capacity and is currently filled with a 40% antifreeze... (answered by nerdybill,josmiceli)
A 15-quart car radiator is full of a solution that is 55% antifreeze and 45% water. The... (answered by josgarithmetic)
A container is filled with 70 liters which is 40% alcohol by volume. How much of a... (answered by ikleyn)
A 16-quart radiator contains a 50% solution of antifreeze. How much needs to be drained... (answered by Mathtut)
An 18 quart radiator contains a 40% solution of antifreeze. How much must be drained out... (answered by checkley77)