Please help me solve this word problem:
A big barrel contains 300 mL of a 6% solution. How much water should be added to obtain a 5% solution?
Suppose the answer is X. That is, if we add X mL of water it
will become a 5% solution
300 mL of a 6% solution, means that the barrel at the start
contains 6% alcohol. Now how many mL is that?
6% of the 300 mL of liquid is .06×300 = 18 mL of alcohol.
If we add X mL of water there will be (300+X) mL of liquid
But there will still be only the same 18 mL of alcohol. So the
statement we will be able to make is
"If X is the right number of mL of water to add, then
18 mL of alcohol will equal to
5% of (300+X) mL of liquid."
That is,
18 = .05(300+X)
Solve that and get the answer as 60 mL of water should be added.
Checking:
If we add 60 mL of water to the 300 mL of liquid, we will then
have 360 mL of liquid.
So the 18 mL of alcohol should be 5% of the 360 mL of liquid,
if we are right.
So we ask "If we take 5% of 360, will we get 18 mL?"
So we multiply .05 times 360, and get 18 mL, so we are right.
Edwin