Apharmacist has an 18% alcohol solution and a 40% alcohol solution. how much of each should he mix together to make 10 liters of a 20% alcohol solution?

Lets call x the amount of 18% solution and y the amount of 40% solution, and write as equations the info of the problem:
18x + 40y = 10(20)
x + y = 10
lets multiply the second equation by -18 and add to the first:
 18x + 40y = 200
-18x - 18y = -180

0 + 22y = 20
y = 20/22 = 10/11
and substitute in the original equation:
x + y = 10
x = 10 - y
x = 10 - 10/11
x = 110/11 - 10/11
x = 100/11
so they have to use 100/11 liters of 18% solution and 10/11 liters of 40% solution

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