% alcohol solution

[JeanneMo]

Ok- here's a new challenge.

" A 5% solution of a drug is to be mixed with some 15% solution and some 10% solution to get 20ml of 8% solution. The amount of the 5% solution used must be 2 ml more than the sum of the other 2 solutions. How many ml of each solution should be used?"

OK I'm not totally dumb. I know that to get the amounts... we need a sum of 20 ml. the sum of 2 of the amounts should be 9ml and the amount of 5% should be 11ml.
SO- is it 8 and 1? 5 and 4? 3 and 6? 2 and 7? and which # goes to the 10% and which to the 15%?

HELP! thanks

 

[Gene]

As with most word problems we need to name things then change the words to math.
Call the 5% A
15% B
10% C
The equations are:
.05A+.15B+.1C=.08*20
A=B+C+2 or A-B-C=2
A+B+C=20
Three equations in three unknowns. Make the first
A+3B+2C=32
That should do it for you.

 

[JeanneMo]

ummm, honestly, I think I'm more confused.

What does that answer have to do with telling me the # of ml of each solution? I was looking for something like... 11 ml 5% 2 ml 10 % 7 ml 15% not necessarily those exact #s but like that vs. 2A + 3B... where does the 32 come in to play?

 

[stapel]

The tutor picked variables for the different amounts, and set up the system of equations for you. Now all you have to do is solve the system.

C'mon: the tutor has already done the hard part! And you should have learned this all back in algebra. You're in calculus now (that's why you posted this algebra question to the "calculus" category, right?), so you should be well able to deal with simple exercises of this sort.

Please read and study the solution provided to you. Then do the one last step to get the final answer. Thank you.

Eliz.

 

[JeanneMo]

I probably don't recall all of this from Algebra because it has been almost 10 years since I took any algebra (or any math course for that matter). I'm working on my masters now and needed one more math credit, but because of what I had taken back when I was in college, this was the lowest they'd let me count towards this degree... it isn't something I use in my profession so it's foreign to me. I appologize for appearing ignorant, but...
Anyway- I've got it figured out.