Problem Solving

a mixture of "lean" ground beef (10% fat) and "super-lean" ground beef (4% fat) contains twice as much lean beed as super-lean beef. What is the percentage of fat in the mixture?


hey guys,

can you explain the LOGIC behind this problem. I know how to do weighted problems, but I don't get how to get the ratio of lean beef to super-lean beef.

please explain

thanks to all.

Super Lean beef=x ,4% fat

Lean beef=2x, 10% fat

Fat in the mixture=4/100*x+10/100*2x

4/100*x+20/100*x

24/100*x

24% of x -->8% of 3x

Hope this clarify

selango wrote:Super Lean beef=x ,4% fat

Lean beef=2x, 10% fat

Hey Anand,

why is lean beef 2x and super lean beef just x.

how do we know what the ratio is between the two? whats confusing me is, the question says that their MIXTURE has twice the beef. so how did you get 2x for lean beef?

that's what i am confused about in this question.

Let the quantity of super lean ground beef be x[like x kg]

Given that mixture contains twice as much lean beed as super-lean beef(ie)Lean beed quantity is twice that of super lean beed.

If the quantity of super lean ground beef be x,then the quantity of lean beef is 2x.[for ex:super lean=2kg,Lean beef=4kg]

The ratio is as below,

Lean beef:Super Lean beef=2:1

Hope this clarify...

selango wrote:Let the quantity of super lean ground beef be x[like x kg]

Given that mixture contains twice as much lean beed as super-lean beef(ie)Lean beed quantity is twice that of super lean beed.

If the quantity of super lean ground beef be x,then the quantity of lean beef is 2x.[for ex:super lean=2kg,Lean beef=4kg]

The ratio is as below,

Lean beef:Super Lean beef=2:1

Hope this clarify...

i am sorry for sounding stupid.....but im still confused....

the way im looking at it is. say

lean B + S-lean B = mixture.
x + 2 = 4 (the 4 is twice that of 2, so its twice the super-lean beef). if i do it this way, i get 2 for x. and therefore i am getting the ratio to be 1:1.

You are taking mixture quantity twice as super lean beef.This is wrong.

Mixture contains lean beef and super lean beef.

Mixture=lean B + S-lean B

Now question states that mixture contains "twice as much lean beed as super-lean beef".

"a twice as much as b" means a=2b

What does "twice as much lean beed as super-lean beef" means?The quantity of lean beef is twice that of super lean beef.It gives us the ratio bw lean and superlean beef.

Lean=2S-Lean

for ex:

superlean beef=2,lean beef=4,Mixture=6

superlean beef=3,lean beef=6,Mixture=9

So the ratio Lean:Superlean is 2:1 or 2x:1x

Let me know if u still have doubts..

selango wrote:You are taking mixture quantity twice as super lean beef.This is wrong.

Mixture contains lean beef and super lean beef.

Mixture=lean B + S-lean B

Now question states that mixture contains "twice as much lean beed as super-lean beef".

"a twice as much as b" means a=2b

What does "twice as much lean beed as super-lean beef" means?The quantity of lean beef is twice that of super lean beef.It gives us the ratio bw lean and superlean beef.

Lean=2S-Lean

for ex:

superlean beef=2,lean beef=4,Mixture=6

superlean beef=3,lean beef=6,Mixture=9

So the ratio Lean:Superlean is 2:1 or 2x:1x

Let me know if u still have doubts..

omg....thanks alot mannn i finally get it know....

i dont know why i was making that silly mistake.

i should bang my head aganist the wall.

thx agian.

Selango,

I don't agree with the answer 24%. You have to divide by 3x at the end to get 8%. You can't have 24% fact by combining two products that individually have 10% and 4% fat contents. It's like thinking that 10 lbs of the lean beef will be 100% fat.

Can't do that.

So Gurpinder the way I solve it is as follows:

Simple weighted average

(2x*10 + x*4) / 3x (I actually don't even use the variable x. You can put any ratio of 2:1.)

You divide by 3x because that is the total quantity of the mixture (x + 2x).

This gives you a percentage of 8% which makes sense because a 50/50 ratio would give you a percentage of 7 and you know that it has to be more than that since there is more lean than super lean.

barcebal wrote:Selango,

I don't agree with the answer 24%. You have to divide by 3x at the end to get 8%. You can't have 24% fact by combining two products that individually have 10% and 4% fat contents. It's like thinking that 10 lbs of the lean beef will be 100% fat.

Can't do that.

So Gurpinder the way I solve it is as follows:

Simple weighted average

(2x*10 + x*4) / 3x (I actually don't even use the variable x. You can put any ratio of 2:1.)

You divide by 3x because that is the total quantity of the mixture (x + 2x).

This gives you a percentage of 8% which makes sense because a 50/50 ratio would give you a percentage of 7 and you know that it has to be more than that since there is more lean than super lean.

oh dammit, i never even looked at selango's answer. I just wanted to get over that confusion that I had. Yes you are right Barcebal. Your answer is the right one.

Gurpinder wrote:a mixture of "lean" ground beef (10% fat) and "super-lean" ground beef (4% fat) contains twice as much lean beed as super-lean beef. What is the percentage of fat in the mixture?


hey guys,

can you explain the LOGIC behind this problem. I know how to do weighted problems, but I don't get how to get the ratio of lean beef to super-lean beef.

please explain

thanks to all.

Another approach would be to plug in our numbers:

200 lean, 100 super lean, total = 300
.1(200) = 20 fat
.04(100) = 4 fat
fat = 20 + 4 = 24
fat/total = 24/300 = 8/100 = 8%

barcebal wrote:Selango,

I don't agree with the answer 24%. You have to divide by 3x at the end to get 8%. You can't have 24% fact by combining two products that individually have 10% and 4% fat contents. It's like thinking that 10 lbs of the lean beef will be 100% fat.

Can't do that.

So Gurpinder the way I solve it is as follows:

Simple weighted average

(2x*10 + x*4) / 3x (I actually don't even use the variable x. You can put any ratio of 2:1.)

You divide by 3x because that is the total quantity of the mixture (x + 2x).

This gives you a percentage of 8% which makes sense because a 50/50 ratio would give you a percentage of 7 and you know that it has to be more than that since there is more lean than super lean.

Yes I missed that one..Edited the post..

GMATGuruNY wrote:

Gurpinder wrote:a mixture of "lean" ground beef (10% fat) and "super-lean" ground beef (4% fat) contains twice as much lean beed as super-lean beef. What is the percentage of fat in the mixture?


hey guys,

can you explain the LOGIC behind this problem. I know how to do weighted problems, but I don't get how to get the ratio of lean beef to super-lean beef.

please explain

thanks to all.

Another approach would be to plug in our numbers:

200 lean, 100 super lean, total = 300
.1(200) = 20 fat
.04(100) = 4 fat
fat = 20 + 4 = 24
fat/total = 24/300 = 8/100 = 8%

this approach is also good ..........thanks..