Problem Solving

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.

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.