## anonymous one year ago 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?

1. phi

160 milliliters of solution that is 25% alcohol by volume. First, how many ml of alcohol do we have ?

2. anonymous

we have 40

3. anonymous

120 of the remainder

4. anonymous

i don't understand why it's not 56

5. phi

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

6. anonymous

160*.6=96-40= 56

7. phi

next , we use this fact: resulting solution is 60% alcohol by volume in other words, the amount of alcohol will be 0.6(160+x) 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)

8. anonymous

why is it 160+x ? sin't 160 the total amount of the solution?

9. anonymous

isnt*

10. phi

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

11. phi

now take 60% of the new amount

12. anonymous

OHHHHHHHHHHHHHHH

13. phi

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.

14. phi

can you solve it?

15. anonymous

16. anonymous

140

17. anonymous

thank u so much phi!

18. 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%

19. anonymous

Yes it works out

20. phi

and 180/300 is 60/100 = 60% so it looks good.

21. anonymous

thank you <333333

22. phi

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.

23. anonymous

Yes Yes will do =)