a flask contains 160 milliliters of solution that is 25% alcohol by volume. How much pure alcohol must be added to the flask so that the resulting solution is 60% alcohol by volume?
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160 milliliters of solution that is 25% alcohol by volume.
First, how many ml of alcohol do we have ?
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i don't understand why it's not 56
ok. now let's add an unknown "x" amount of alcohol, so that we have
40+ x ml of alcohol
of course, we have to pour the x ml of alcohol into the mixture
so the mixture has 160+x ml
next , we use this fact:
resulting solution is 60% alcohol by volume
in other words, the amount of alcohol will be
and that has to equal 40+x
in other words, the equation is
0.6(160+x) = 40 + x
now we use algebra to solve for x (amount of alcohol to add)
why is it 160+x ? sin't 160 the total amount of the solution?
we start with 160 (which is 40 alcohol and 120 water?)
unfortunately it is all mixed together. But if we add pure alcohol, the percent of alcohol goes up. For example if we add lots and lots of alcohol, the mixture becomes more alcohol.
so pour in x of pure alcohol into the mixture
we have 160+x ml total now
now take 60% of the new amount
0.6(160+x) = amount of pure alcohol
the amount of alcohol will be 40 (the amount in the original) + x (the amount we added)
0.6(160+x) = x+ 40
the thinking might be confusing, but if you see it, it is quite nice.
can you solve it?
sorry i hadda help my dad with some tools
thank u so much phi!
Let's see if it makes sense.
The new mixture has 160+140= 300 ml of liquid
we know we have 40 ml of alcohol (from the original 160) and we add 140 ml of alcohol
so it has 40+140= 180 ml of alcohol
if we did it right, 180/300 should be 60%
Yes it works out
and 180/300 is 60/100 = 60% so it looks good.
thank you <333333
Now that the answer makes sense, review your thinking about how to do it. And try to remember what confused you. That is what I do to try to learn the idea.