The mixture of glue and vinegar is 20kg and 30% of it is glue. It got added 22kg of vinegar afterwards. To make it 60% of vinegar, how much glue should we add?

Question

hero · Answer

g = amount of glue in kilograms
v = amount of vinegar in kilograms

g + v = 20
g = .30(20) = 6
v = 14

I was able to determine this much about the problem. The part where it says "It got added 22kg of vinegar afterwards"

That's where it starts getting fuzzy. Something about that sentence makes it seem like it was written by a fifth grader.

anonymous · Answer

well, its a fifth grader problem. and I translated it from another language so it will be hard to hard to understand, sorry

hero · Answer

Okay, I'll try my best.

anonymous · Answer

mmm, okay

hero · Answer

Seems like 22 kg of vinegar was added so:

6 + (14 + 22) = 42
6 + (36) = 42

hero · Answer

36 is the total amount of vinegar we have now.

anonymous · Answer

yeah, ok

hero · Answer

We only have 6 kg of glue

anonymous · Answer

right

hero · Answer

So now we need to figure out how much glue we need to add for the mixture to be 60% vinegar.

anonymous · Answer

yes, and that's where I got stuck

anonymous · Answer

yeah

anonymous · Answer

ok, alright

hero · Answer

But wait...something isn't adding up here.

anonymous · Answer

Ok, what?

hero · Answer

The vinegar is going to be 60% of the total kg amount

anonymous · Answer

yeah, that's correct.

hero · Answer

But something still doesn't make sense about it.

hero · Answer

I'm still trying to figure it out

anonymous · Answer

I know! I think its a writing error.

hero · Answer

No, unfortunately it's not.

anonymous · Answer

So, it's that hard.

hero · Answer

No, it's not. We're both just making it hard.

anonymous · Answer

How?

hero · Answer

I think we have to solve it by setting up a ratio

anonymous · Answer

Ok, let's try.

hero · Answer

The mixture of glue and vinegar is 20kg and 30% of it is glue. It got added 22kg of vinegar afterwards. To make it 60% of vinegar, how much glue should we add?


Originally 

The ratio of glue to vinegar is $$\frac{6}{14}$$ So 30% of the mixture is glue 70% is vinegar.

After adding 22 kg of vinegar we have

$$\frac{6}{36}$$

anonymous · Answer

yeah, so, is that the last answer?

hero · Answer

Now we have to add a certain amount of glue for the percentage to be 40% glue and 60% vinegar

$$\frac{6 + g}{36} = \frac{40%}{60%}$$


@babybluepies , patience...We're figuring this out together.

hero · Answer

$$\frac{6 + g}{36} = \frac{.40}{.60}$$

hero · Answer

That should be the right setup. I had that the first time but my percentage symbols didn't show up

anonymous · Answer

Thanks! i think I figured it out now, you really are a hero!

hero · Answer

You should be able to use that to solve for g

hero · Answer

Let me know what you get for g

anonymous · Answer

Okay, give me a moment.

anonymous · Answer

Kay, I got the answer but the thing is its a negetive number is that okay? The answer is 4.

anonymous · Answer

-4

hero · Answer

No, there's no possible way to get that. You have some issues with your algebra.

anonymous · Answer

Okay, harsh,but I'll check it again.

hero · Answer

All you had to do is cross multiply and simplify. Then isolate g.

hero · Answer

I did all the hard work for you already.

anonymous · Answer

Ok, sorry.

hero · Answer

I think you are stuck

hero · Answer

I'm going to finish solving it. I thought you had it from here.

hero · Answer

$$\frac{6 + g}{36} = \frac{.40}{.60}$$

Cross multiply:
.6(6 + g) = .4(36)
3.6 + .6g = 14.4
.6g = 14.4 - 3.6
.6g = 10.8
   g = 10.8/.6
   g = 108/6
   g = 18