SOLUTION: three solutions contain a certain acid. the first contains 15% acid, the second 35%, and the third 40%. A chemist wishes to use all three solutions to obtain a 75-liter mixture con

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Question 744940: three solutions contain a certain acid. the first contains 15% acid, the second 35%, and the third 40%. A chemist wishes to use all three solutions to obtain a 75-liter mixture containing 34% acid. If the chemist wants to use twice as much of the 35% solution as of the 40% solution, how many liters, to the nearest 10th, of each solution should be used?
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = liters of 40% solution needed
= liters of 35% solution needed
Let = liters of 15% solution needed
---------------
= liters of acid in 40% solution
= liters of acid in 35% solution
= liters of acid in 15% solution
----------------
(1)
(2)
----------------
(1)
and
(2)
(2)
(2)
----------------
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)

and, since
(1)
(1)
(1)
(1)
21.9 liters of 40% solution are needed
43.8 liters of 35% solution needed
9.2 liters of 15% solution are needed
--------------
check:
(2)
(2)
(2)
(2)
OK