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Mixture Problem help

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by infiniti007 » Wed Feb 25, 2015 6:08 pm
Hi, I was looking to see if I could get some help on how to setup and solve a mixture problem I recently encountered. The question follows:

A mixture of ground meat consists of 2 pounds of veal that costs x dollars per pound, and 5 pounds of beef that costs y dollars per pound. What is the cost of the mixture in dollars per pound?

A) 2x + 5y
B) 2x + 5y / xy
C) 5(2x + 5y)
D) x + y
E) 2x + 5y / 7

I was able to setup an equation that says:
2x + 5y = 7

But how do I move from there? I feel like this problem is fairly intuitive, but for some reason it's tripping me up a bit. Any help or insight on how to approach would be much appreciated.
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by [email protected] » Wed Feb 25, 2015 6:32 pm
Hi infiniti007,

It's important to be clear on what the variables represent. X and Y are both COSTS of meats.

This question asks us to mix 2 pounds of veal and 5 pounds of beef, so the total WEIGHT = 7 pounds

The cost per pound will = (Total Cost)/(Total Weight)

Veal is X dollars per pound. 2 pounds of Veal costs 2X
Beef is Y dollars per pound. 5 pounds of Beef costs 5Y

Total Cost = 2X + 5Y

Total Cost per pound = (2X + 5Y)/7

Final Answer: E

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by GMATGuruNY » Wed Feb 25, 2015 7:46 pm
infiniti007 wrote:A mixture of ground meat consists of 2 pounds of veal that costs x dollars per pound, and 5 pounds of beef that costs y dollars per pound. What is the cost of the mixture in dollars per pound?

A) 2x + 5y
B) 2x + 5y / xy
C) 5(2x + 5y)
D) x + y
E) 2x + 5y / 7
An alternate approach is to plug in values.

Let x=5 and y=10.
At a cost of $5 per pound, the total cost for 2 pounds of veal = 5*2 = 10.
At a cost of $10 per pound, the total cost for 5 pounds of beef = 10*5 = 50.
Cost per pound = (total cost)/(total weight) = (10+50)/(2+5) = 60/7, This is our target.

Now plug x=5 and y=10 into the answers to see which yields our target of 60/7.
A quick scan of the answer choices reveals that only E will yield a denominator of 7.

The correct answer is E.
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by Brent@GMATPrepNow » Thu Feb 26, 2015 9:26 am
infiniti007 wrote: A mixture of ground meat consists of 2 pounds of veal that costs x dollars per pound, and 5 pounds of beef that costs y dollars per pound. What is the cost of the mixture in dollars per pound?

A) 2x + 5y
B) (2x + 5y)/xy
C) 5(2x + 5y)
D) x + y
E) (2x + 5y)/7
We can use the WEIGHTED AVERAGE formula:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

When we COMBINE the meats, the TOTAL weight = 2 + 5 = 7 pounds.
So, veal comprises 2/7 of the TOTAL mixture
Beef comprises 5/7 of the TOTAL mixture

Plug values into formula:

Weighted average of groups combined = (2/7)(x) + (5/7)(y)
= 2x/7 + 5y/7
= (2x + 5y)/7
= E

---------------------------------------

For more information on weighted averages, you can watch this free GMAT Prep Now video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-ave ... 17237.html
- https://www.beatthegmat.com/weighted-ave ... 14506.html
- https://www.beatthegmat.com/average-weig ... 57853.html
- https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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