A pharmacist has a 40% acid solution and a 25% acid solution. How many liters of each must be mixed to form 149 liters of a 30% acid solution?

Question

phi · Answer

That answer came out amazingly close, even though it was done wrong.  I think you should equate the amount of acids. Something like
let x= amount of .4 acid,  y= 0.25 acid
and the total amount of 0.3 acid is (x+y)

anonymous · Answer

Didn't we just have this?

anonymous · Answer

That answer came out amazingly close, even though it was done wrong. I think you should equate the amount of acids. Something like let x= amount of .4 acid, y= 0.25 acid and the total amount of 0.3 acid is (x+y)

anonymous · Answer

40x +25y = 149.30, x+y = 149

15x + 25.149 = 149.30
x = 149.5/15 = 149/5 = 49 and 2/3 so y is 99 and 1/3

(Not really sure about it, check it).

anonymous · Answer

I have been struggling with this one, just can't quite figure it out

phi · Answer

Pretty close, but no cigar.  First, I would use 0.40 and 0.25, not 40 and 25, just to keep things clear.

The starting equations are
0.4 x + 0.25 y = 0.3(x+y)
x+y = 149
The first equation says the amount of acid in x + the amount in y = the amount in x+y
to solve, replace x+y with 149, and y with 149-x.

To check the answer, the total amount of acid = 0.4x+0.25y divided by 149 better be 30% = 0.30

anonymous · Answer

awesome, i was very close i just didn't have the .3(x+y) thank you so much that really helped

anonymous · Answer

@phi
"The starting equations are 0.4 x + 0.25 y = 0.3
(x+y) x+y = 149"

Those are the same as mine...

phi · Answer

The right hand side is not 0.3, it is 0.3*149
= 44.7 not 30

anonymous · Answer

that's 149 * 30!!!

phi · Answer

I was confused by the formatting. For example you wrote 149.5/15 , which I interpreted as a decimal 149 and one-half.  I might have figured it out, but when you wrote 149.5/15 = 149/5 I completely lost the bubble.  Now I see it was a simple mistake.

anonymous · Answer

I also gave the answer, which is correct.

phi · Answer

My apologies. You did give the correct numbers.

anonymous · Answer

i appreciate all of your help, I too misunderstood the format

anonymous · Answer

@phi
Accepted:-)