From a tank filled with 240 gallons of alcohol, 60 gallons are drawn off and the tank is filled up with water. Then 60 of the mixture are removed and replaced with water, etc. How many gallons of alcohol remain in the tank after 5 drawings of 60 gallons each are made?
Answers
Given : a tank filled with 240 gallons of alcohol, 60 gallons are drawn off and the tank is filled up with water. Then 60 of the mixture are removed and replaced with water
To find : How many gallons of alcohol remain in the tank after 5 drawings of 60 gallons each are made?
Solution:
Initially
Alcohol = 240 Gallons Water = 0 Gallons
After 1st Draw
Alcohol = 180 Gallons Water = 60 Gallons
After 2nd Draw
Alcohol = 180 - ( 180/240)* 60 = 135 Gallons
Water = 60 - (60/240)60 + 60 = 105 Gallons
After 3rd Draw
Alcohol = 135 - ( 135/240)* 60 = 135(3/4) Gallons
After 4th Draw
Alcohol = 135(3/4) - ( 135(3/4)/240)* 60 = 135(3/4)² Gallons
After 5th Draw
Alcohol = 135(3/4)² - ( 135(3/4)²/240)* 60 = 135(3/4)³ Gallons
= 56.95 gallons
or Simply Alcohol remains after each draw
= A - (A/240)* 60 = (3/4)A
Alcohol remains after 5 draw = A(3/4)⁵
= 240 * (3/4)⁵
= 56.95 gallons
56.95 gallons of alcohol remain in the tank after 5 drawings of 60 gallons each are made
learn more:
21. A mixture "M1" of Mix Juice, Orange Juice and Pineapple Juice ...
https://brainly.in/question/12864600
two mixtures equal quantity contain wine,water ,alcohol in the ratio ...
https://brainly.in/question/17155212