Question 1184009: How many quarts of pure antifreeze must be added to 5 quarts of a 30% antifreeze solution to obtain a 50% antifreeze solution Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
A classic formal algebraic solution would go something like this....
You are mixing 5 quarts that is 30% antifreeze and x quarts that are 100% antifreeze to get (5+x) quarts that is 50% antifreeze:
ANSWER: 2 quarts
An informal method that will give you the answer within 15 seconds if you understand it....
(1) Look at the three percentages 30, 50, and 100 on a number line and observe/calculate that 50 is 2/7 of the way from 30 to 100. (30 to 100 is a difference of 70; 30 to 50 is a difference of 20; 20/70 = 2/7.)
(2)That means 2/7 of the mixture is the 100% antifreeze that you are adding.
(3) So the 5 quarts you started with is 5/7 of the mixture; that means 2/7 of the mixture is 2 quarts.
You can put this solution on YOUR website! .
How many quarts of pure antifreeze must be added to 5 quarts of a 30% antifreeze solution
to obtain a 50% antifreeze solution
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In my previous post, I gave a detailed description of the solution procedure to a TWIN problem in word form.
THEREFORE, I will omit here all the words and will present the solution in short form.
The basic equation is
= 0.5
x + 0.3*5 = 0.5*(x+5)
x + 1.5 = 0.5x + 2.5
x - 0.5x = 2.5 - 1.5
0.5x = 1.0
x = = 2.
ANSWER. 2 quarts of the pure antifreeze must be added.
CHECK. = = = 0.5 = 50% ( ! correct concentration ! )
