Question

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

Answer 1

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

Answer 2

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

Answer 3

Make sense so far?

Answer 4

yes

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

@Catseyeglint911?

Answer 10

sorry I had to step a way for a bit

Answer 11

No worries :)

Answer 12

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

Answer 13

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?

Answer 14

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?

Answer 15

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.

Answer 16

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

Answer 17

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)

Answer 18

The 50 to a 50+x

Answer 19

Do you follow me?

Answer 20

Ooohhh! I see now. :D

Answer 21

:D

Answer 22

Can you solve for x?

Answer 23

(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?

Answer 24

Awesome! :)

Answer 25

Thank you so much. :)

Answer 26

No worries