Different approaches to a problem

[jimmiejaz]

Hi guys,

I am stuck at this problem. I can figure this with the basic weighed avges but i want to know how to solve this problem if we take 100 and 200 gallons as 0 and 100 respectively and i am getting 35% instead of 30%.
Wat's the fault in my approach. please explain.

Mixture M consists of 65% water and 35% ethanol. Mixture N
consists of 80% water and 20% ethanol. If 200 gallons of
Mixture M is combined with 100 gallons of Mixture N, what
percent of the resulting solution is ethanol?

Approach one:
(.35*200+.2*100)/300 = 30%

Approach 2:
(.35*100+.2*0)/100 = 35%

why is the answer diff this time?
I am unable to figure out!!!!

[joanjgonzalez]

Hi Jimmiejaz,

I would say the correct approach is #1. In you 2nd approach you are mixing 100 gallons of M solution with no gallons (zero in your formula) of N mixture. Therefore, you obtain 35% solution. Note that this percentage corresponds to the percentage of the first solution and that that is obvious because you have mixed it with 0 liters of N (no N mixture).


Hope it is useful,

JJ

[Stuart@KaplanGMAT]

Hi guys,

I am stuck at this problem. I can figure this with the basic weighed avges but i want to know how to solve this problem if we take 100 and 200 gallons as 0 and 100 respectively and i am getting 35% instead of 30%.
Wat's the fault in my approach. please explain.

Mixture M consists of 65% water and 35% ethanol. Mixture N
consists of 80% water and 20% ethanol. If 200 gallons of
Mixture M is combined with 100 gallons of Mixture N, what
percent of the resulting solution is ethanol?

Approach one:
(.35*200+.2*100)/300 = 30%

Approach 2:
(.35*100+.2*0)/100 = 35%

why is the answer diff this time?
I am unable to figure out!!!!

If you change the ratio of the solution, of course you're going to get a different weighted average. The question clearly states how much of each mixture you're using, so I'm not sure why you'd want to change the numbers.

If you had kept the ratio the same, e.g. chosen 100M and 50N, you would have gotten the same result as the original. You changed a 2:1 ratio to a 1:0 ratio, something that violates the terms of the question.

[jimmiejaz]

Thanks for the explanation stuart.

I was attempting this concept.
2 things cost 170 3 cost 180 wats the avg.
we can do it as
(2*0 + 3*10)/5 = 6
so avg is 176

How to apply it here?
OR Can i apply this approach on these type of questions?