SOLUTION: A chemist has one solution that is 20% acid and a second that is 65% acid. How many gallons of each should be mixed together to get 120 gallons of a solution that is 50% acid?

Question 551101: A chemist has one solution that is 20% acid and a second that is 65% acid. How many gallons of each should be mixed together to get 120 gallons of a solution that is 50% acid?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = gallons of 20% solution needed
Let = gallons of 65% solution needed
= gallons of acid in 20% solution
= gallons of acid in 65% solution
given:
(1)
(2)
-------------------------
(2)
(2)
(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)

and, since
(1)
(1)
(1)
(1)
40 gallons of 20% solution are needed
80 gallons of 65% solution are needed
check answer:
(2)
(2)
(2)
(2)
(2)
OK
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