Question

will medal
Marie mixes 16 liters of 78% acid solution with a 25% acid solution to make a 41% acid solution.
How many liters of 25% solution did she use?



8 liters


12 liters


13.7 liters


37 liters

Answer 1

Alright, so what I did was set up a proportion after calculating a %

So first, would you know how to find out many liters were acid out of the 16? Basically, can you find what 78% of 16 is?

Answer 2

To find out a percentage of a number, you take the number and multiply it by the decimal of the percentage over 1

So 78% would turn into .78, like you're just putting a dot in front of it. So you would do 16 times .78

Answer 3

1248

Answer 4

Yeah, but with the dot, it'll be 12.48
Now that we found this we can put it over 16.00, because that's the total amount of solution we have

12.48
-----
16.00

Now they give you another total, which is 41% and they want to know how many liters it took to make the solution 25%. So first let's solve a proportion

12.48 25.00
----- = ----
16.00 x

Would you know how to solve this? With cross multiplying and dividing?

Answer 5

Sorry for the delay, I forgot how I solved it myself lol

Answer 6

yea no I don't know how to solve that

Answer 7

is the second part like the first part where I have to times it?

Answer 8

Yes, but you would do it to the 25 and 16 since they are "crossing" each other.
After you do that, you would divide that by 12.48, giving you X

Answer 9

? I got 32.05 16 x 25 = 400 (even when it is 16.00 and 25.00) and then divide it by 12.48 and I got 32.05?

Answer 10

another approach would be to build an equation:-

work in wieghts of pure acid

16*0.78 + 0.25x = 0.41( 16 + x)

where x is the volume of the 25% acid

Answer 11

Yep. The 32.05 is 100% solution, but they asked for 25% solution. So what would you do?

Omg I like welsh's approach. I really should learn now to over complicate things >__>

Answer 12

Yea - try to make it as simple as possible.

Answer 13

16*0.78 + 0.25x = 0.41( 16 + x)
12.48 + 0.25x = 0.41x + 6.56
5.92 = 0.16x

x = 5.92/0.16

Answer 14

37 liters