Mixture Problem

[marion.roth]

I have a problem with the following question:
A drink contains 40% gin and 60% vodka. If the volume of the drink is (n) how much vodka must be added in terms of (n) to be left with a 25% concentration of gin? The answer is 3/5n.

Can someone explain how to solve this problem?

[hardykarim]

In the first mixture you have
40% gin + 60% vodka for n volume of drink. Therefore:
volume of gin=0.4n
volume of vodka=0.6n

Let x, the volume added.

So for the new mixture the total volume is n+x and we know that we have 25% of gin = 0.25(n+x)

We added only vodka therefore the volume of gin is the same:

0.4n=0.25(n+x)

x=0.15n/0.25=3n/5

[jnelson0612]

I have a problem with the following question:
A drink contains 40% gin and 60% vodka. If the volume of the drink is (n) how much vodka must be added in terms of (n) to be left with a 25% concentration of gin? The answer is x3/5n.

Can someone explain how to solve this problem?

I like to plug in numbers. I would say that n=10 cups. Thus, the drink has 4 cups of gin and 6 cups of vodka.

I want to add vodka so the gin becomes 25% of the drink. If I have 4 cups of gin and that is going to be 25% of the new drink, the new drink must be 16 cups. Thus I had to add 6 cups of vodka, or 3/5(n) since we decided that n=10.

[THANU.KG]

Hi Jamie,

can you please explain how you came to a conclusion that you should add 6 cups of vodka to the new drink. If the new drink must be 16 cups, and gin remains the same 4 cups (which is 25%), then shouldn't the vodka be 12 cups?

Or is it that, I already had 6 cups with me, so I need 6 more to make 16 cups.

Please confirm.

Thanks

[jnelson0612]

Hi Jamie,

can you please explain how you came to a conclusion that you should add 6 cups of vodka to the new drink. If the new drink must be 16 cups, and gin remains the same 4 cups (which is 25%), then shouldn't the vodka be 12 cups?

Or is it that, I already had 6 cups with me, so I need 6 more to make 16 cups.

Please confirm.

Thanks

Hi Thang,
Certainly; let's review.

I decide that my original drink is 10 cups. Since I am told that 40% is gin and 60% is vodka, 4 cups will be gin and 6 will be vodka.

I am going to add vodka so that the new drink is 25% gin. Thus, if 4 cups of gin is 25% of the drink, the new drink must contain 16 cups total, or 4 cups of gin and 12 cups of vodka. Thus, I added 6 cups of vodka to the original mixture.

Hope this helps! :-)