## Catseyeglint911 one year ago Who wants a medal? How much of a 60% acid solution must be mixed with 50 gallons of a 24% acid solution to obtain a solution that is 50% acid? a. 130 gal c. 13 gal b. 125 gal d. None of these

1. JoannaBlackwelder

I would use the idea of a mass balance of the acid.

2. JoannaBlackwelder

For example, the amount of acid in the 50 gallons of a 24% acid solution would be 50*.24=12 gallons of acid.

3. JoannaBlackwelder

Make sense so far?

4. Catseyeglint911

yes

5. JoannaBlackwelder

Sweet. Since we don't have the volume of the 60% acid solution, I will call that x.

6. JoannaBlackwelder

Can you write an expression that shows the volume of acid of the 60% acid solution?

7. Catseyeglint911

0.5 = 0.6x + (50*0.24) I have a feeling that this isn't right.

8. JoannaBlackwelder

That is close. The addition side looks good, but what about the volume of the combined solution?

9. JoannaBlackwelder

@Catseyeglint911?

10. Catseyeglint911

sorry I had to step a way for a bit

11. JoannaBlackwelder

No worries :)

12. Catseyeglint911

(0.5*50) = 0.6x + (50*0.24) Is this what you meant?

13. JoannaBlackwelder

Closer. :) The volume of the 24% solution is 50 gals and the 60% acid solution has volume x gals, so wouldn't the combined 50% acid solution have more volume that 50 gals?

14. Catseyeglint911

So we would have to use two variables since we don't know the number of gallons need of the 60% solution nor do we know the number of gallons of the final solution?

15. JoannaBlackwelder

We could, but we don't have to. Since we know we are adding two volumes together and one volume is 50 gallons and we defined the second volume to be x gallons. So the combined volume is 50+x gallons.

16. Catseyeglint911

(x+50) = 0.6 + (50*0.24) It's still wrong isn't it?

17. JoannaBlackwelder

Last time you put (0.5*50) = 0.6x + (50*0.24) which was closer. The only thing you needed to change was (0.5*[50+x]) = 0.6x + (50*0.24)

18. JoannaBlackwelder

The 50 to a 50+x

19. JoannaBlackwelder

20. Catseyeglint911

Ooohhh! I see now. :D

21. JoannaBlackwelder

:D

22. JoannaBlackwelder

Can you solve for x?

23. Catseyeglint911

(0.5*[50+x]) = 0.6x + (50*0.24) 25 + 0.5x = 0.6x + 12 13 + 0.5x = 0.6x 13 = 0.1x 130 = x right?

24. JoannaBlackwelder

Awesome! :)

25. Catseyeglint911

Thank you so much. :)

26. JoannaBlackwelder

No worries