How would you solve this problem

[Pierre.Suave]

today is my day to not get math I guess, but here it is...

How many fluid ounces of pure acid (100%) must be added to 60 ounces of a 20% acid solution to obtain a 40% acid solution?

the answer (according to the book) is 20 ounces, but how do you get there...

[SKKY]

1. Um, 10 ounces?

let's see, 60 ounces of something with a 20% acidity, plus another 10% of pure acid, giving you 70 ounces with a 30% acidity? It makes sense in my world.

[Pierre.Suave]

2. nope

not according to my book.

plus, if you added 10 ounces of acid to the 60 ounces you would have 70 ounces of solution with 30 ounces of acid would be a 42.8% solution, 43% if you round up.

[Phillycat]

3. Don't take the brown acid, man!

[Tuesday Afternoon]

4. because at 100%, the ratio would be 1:1

therefore to get to 20+20=40.

[Pierre.Suave]

6. ok, am I really this dense?

or is it really that easy...

Do I really need sleep?

[Tuesday Afternoon]

7. Well,

You gave the answer :blush:

[Pierre.Suave]

8. Well, I know the answer

and I checked it to ensure it is right, but I was stumped trying to get there.

[DarkTirade]

5. Heh, I just dozed through one of those problems in class today...

lemme see if I can remember it from last semester... :P

[DarkTirade]

10. ...

How many fluid ounces of pure acid (100%) must be added to 60 ounces of a 20% acid solution to obtain a 40% acid solution?

Okay, let's start from the beginning. You're looking for ounces of pure acid. So X=ounces of pure acid.

X + .2(60)= .4(X+60)

Now, on the left side you have the two solutions. The X one is 100%, so it's technically 1X + .2(60), but I just left the 1 off.

On the right you have the end result. A 40% solution that is made up of the total number of ounces of the two solutions combined.

You should be able to just solve for X from there.

X + 12 = .4X + 24

.6X + 12=24

.6X = 12

X = 20

[KitchenWitch]

9. Never mind...

1x + .2(60) = .4x

1x + 12.0 = .4x

Solve for x

[Orrex]

12. Spare us your witchcraft, you math harlot

Burn her!

[Orrex]

11. 60 ounces

[Pierre.Suave]

13. Very funny

but sorry, no.


However, I am sure you knew that...


:rofl:

[Orrex]

15. Just double everything, right?

It's even easier if you start with 200% pure acid.

[Pierre.Suave]

17. Ohhh

Concentrated acid, awesome...

:rofl:

[Inchworm]

14. ok, that was fun to stare at before sleeping

I used to know, but I bet my dreams will be cool tonight :)

:yourock:

[KitchenWitch]

16. Showing my work

x + .2*60 = .4(x+60)

x + 12 = .4x + 24

x = .4x + 12

.6x = 12

x = 20

[Pierre.Suave]

19. Ok Ok brainy pants...

thanks...

:P

[KitchenWitch]

20. You wanted the solution right?

[Pierre.Suave]

21. Yes

thank you, I appreciate it, I had a huge mental block on this problem tonight.

[KitchenWitch]

22. The basic algebra can be maddening in its simplicity.

[Pierre.Suave]

23. I think I am just way too tired right now

to even think straight...

[pokerfan]

18. ok

You have 60 oz that is 20% acid. That means 12 oz of that 60 is acid.

You add x oz of acid you have a concentration of (12 + x)/(60 + x)

Set that equal to 40% and solve...

.40 = (12 + x)/(60 + x)
.40(60 + x) = 12 + x
24 + .4x = 12 + x
12 = .6x
x = 20

[Inchworm]

24. I like your proof bestest

brainiac's upthread was sooo numbery :D

:hide:

[pokerfan]

26. I'm not very smart so I have to make it really simple

[KitchenWitch]

27. who is the brainiac?

[Pierre.Suave]

29. Orrex

just look at his answers...

:P

[Inchworm]

30. huh, what, umm

*points over there*

:yoiks:














:P

[Pierre.Suave]

28. Thanks

I get it now, and should have a lot sooner...

:banghead:

[DarkTirade]

25. Teacher, teacher, everyone's copying me!

:P