Question 1147529: An engine has a 4.4 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 62.1 % solution (a mix of 62.1 % pure antifreeze and 37.9 % water). How much pure antifreeze (in litres) must be combined with a 31.4 % solution to achieve 4.4 litres of the ideal solution?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! capacity of the cooling system is 4.4 liters.
most ideal solution is 62.1% pure antifreeze.
you have x liters of a 31.4% solution.
you want to know how many liters of pure antifreeze you need to add to this to get 4.4 liters of 62.1% solution.
let y = the number of liters of pure antifreeze (100% antifreeze).
your equations are:
x + y = 4.4
.314 * x + y = .621 * 4.4
multiply both sides of the first equation by .314 and leave the second equation as is (after simplification) to get;
.314 * x + .314 * y = 1.3816
.314 * x + y = 2.7324
subtract the first equation from the second to get:
.686 * y = 1.3508
solve for y to get:
y = 1.3508 /.686 = 1.96909621.
since x + y = 4.4, then x must be equal to 4.4 minus y = 2.43090379.
confirm by replacing x and y with those values in the two original equations to get:
2.43090379 + 1.96909621 = 4.4
.314 * 2.43090379 + 1.96909621 = 2.7324.
since .621 * 4.4 = 2.7324, both original equations are correct when x and y are replaced with their respective values, as shown below:
x = 2.43090379
y = 1.96909621
you need to add 2.43090379 liters of 31.4% solution with 1.96909621 liters of pure antifreeze to get 4.4 liters of 62.1% solution.
the amount of pure antifreeze is .314 * 2.43090379 + 1.96909621 = 2.7324
2.7324 / 4.4 = .621 * 100 = 62.1%.
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