SOLUTION: Tank a contains 32 gallons of solution which is 25% alcohol by volume. Tank b has 50 gallons of solution which is 40% alcohol by volume. What volume should be taken from each tank

Algebra ->  Test -> SOLUTION: Tank a contains 32 gallons of solution which is 25% alcohol by volume. Tank b has 50 gallons of solution which is 40% alcohol by volume. What volume should be taken from each tank       Log On


   

Question 399317: Tank a contains 32 gallons of solution which is 25% alcohol by volume. Tank b has 50 gallons of solution which is 40% alcohol by volume. What volume should be taken from each tank and combined in order to make up 40 gallons of solution containing 30% alcohol by volume?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons to be removed from tank a
Let b = gallons to be removed from tank b
.25a = gallons of alcohol removed from tank a
.4b = gallons of alcohol removed from tank b
--------------------------------------------------
%28.25a+%2B+.4b%29%2F40+=+.3
.25a+%2B+.4b+=+12
(1) 25a+%2B+40b+=+1200
also,
(2) a+%2B+b+=+40
Multiply both sides of (2) by 25
and subtract (2) from (1)
(1) 25a+%2B+40b+=+1200
(2) -25a+-+25b+=+-1000
15b+=+200
b+=+13.333
And from (2),
a+=+40+-+b
a+=+40+-+13.333
a+=+26.666
combine 26 2/3 gallons from tank "a"
with 13 1/3 gallons from tank "b"
check answer:
%28.25a+%2B+.4b%29%2F40+=+.3
%28.25%2A26.666+%2B+.4%2A13.333%29%2F40+=+.3
.25%2A26.666+%2B+.4%2A13.333+=+12
+6.666+%2B+5.333+=+12
12+=+12
OK