Question

How do I set this up?
one solution containing 20 percent alcohol is mixed with another solution containing 60 percent alcohol to make 10 gallons of a solution that is 32 percent alcohol. How much of each solution is used?

Answer 1

\[0.6x+0.2(10-x)=.32\times10\] is a good start

Answer 2

if you call the amount of 60% solution \(x\) then since the total is 10, the amount of 20% solution must be \(10-x\)

Answer 3

then 60% of the 60% solution is alcohol, 20% of the 20% solution of alcohol and the total when mixed together is 32% of 10, which is 3.2

Answer 4

to solve start with
\[0.6x+0.2(10-x)=.32\times10\] or
\[0.6x+0.2(10-x)=3.2\]then multiply both sides by 10 to clear the decimals and get
\[6x+2(10-x)=32\] and now it should be straight forward