mixture problem: mixture contain 80% husk and 20%sand

[Deepak_J_Shah]

Que from:
http://gmatclub.com/forum/mixture-probl ... ml#p581540

if 200 lb of a mixture contain 80% husk and 20%sand. Then how much husk needs to be extracted in order to have 75% concentration of Husk?

1/4
20/3
1/2
40
60

can someone please solve this algebraically?
thanks in advance.
(I am getting 40 - but i dont like that method)

[kinjal.nandy]

let x be the amount that needs to be extracted.
80% of 200 is 160 and 20% of 200 is 40
now the remaining amount of solution would be 160-x+40= 200-x
the equation forms as
75%(final amount)=final amount of husk
3/4(200-x)=160-x
=> x=40

hopefully this explains to you.

[RonPurewal]

you should make an RTD STYLE TABLE for this problem. instead of labeling the columns as "rate", "time", and "distance", label them as "% husk", "total lbs", and "lbs of husk". then, just as in rtd problems, the product of the first two columns equals the third column.

here's how the table looks (note that it won't line up when it's typed on here)

----------- % HUSK ---- TOTAL LBS ---- LBS OF HUSK ---
original ----- 0.80 ----- 200 ------------ 160
extracted ---- 1 --------- x -------------- x
new --------- 0.75 ------ 200 - x ---------- 160 - x

the last two entries were gotten from the fact that you can subtract pounds.

therefore:
(0.75)(200 - x) = 160 - x
150 - 0.75x = 160 - x
0.25x = 10
x = 40

--

by the way, you may want to solve this problem by PLUGGING IN THE ANSWER CHOICES AND WORKING BACKWARDS.

start with the middle choice (in numerical order, not necessarily in order of presentation**), which is apparently 20/3. if you actually DO this - i.e., take away 20/3 lbs of husk - then you'll find that the % husk is still greater than 75%. therefore, you didn't remove enough husk. this eliminates 20/3 AND both of the choices that are smaller than 20/3.
then try 40. you'll find that it works: taking away 40 lbs of husk gives 160 total lbs left, of which 120 are husk. that's exactly 75%, as needed.

**on a real gmat problem, these numbers will ALWAYS be presented in order. the only problems on which the numbers are NOT in order are problems on which putting the numbers IN order would give away the answer to the problem, i.e., "which of these fractions is second biggest?".
also, there is no way the gmat would include the obviously incorrect answers of 1/4 lb and 1/2 lb. these are RIDICULOUSLY small amounts, which would lead to negligible changes in the % husk.