If a mixture of ground meat consists of 2 pounds of veal...

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If 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, in dollars, per pound of the mixture?

$$A.\ 2x\ +\ 5y$$
$$B.\ \frac{2x+5y}{xy}$$
$$C.\ 5\left(2x+5y\right)$$
$$D.\ x+y$$
$$E.\ \frac{2x+5y}{7}$$

The OA is E.

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LUANDATO 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?

$$A.\ 2x\ +\ 5y$$
$$B.\ \frac{2x+5y}{xy}$$
$$C.\ 5\left(2x+5y\right)$$
$$D.\ x+y$$
$$E.\ \frac{2x+5y}{7}$$
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

Answer: E

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by Jeff@TargetTestPrep » Thu Mar 22, 2018 2:50 pm
LUANDATO wrote:If 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, in dollars, per pound of the mixture?

$$A.\ 2x\ +\ 5y$$
$$B.\ \frac{2x+5y}{xy}$$
$$C.\ 5\left(2x+5y\right)$$
$$D.\ x+y$$
$$E.\ \frac{2x+5y}{7}$$
Let's assume that we have 7 pounds of the meat mixture, which would consist of 2 pounds of veal and 5 pounds of beef. The cost of the 7-pound mixture would thus be (2x + 5y). Therefore, the cost of one pound of the mixture is (2x + 5y)/7 dollars.

Answer: E

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