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If a mixture of ground meat consists of 2 pounds of veal that costs x

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If a mixture of ground meat consists of 2 pounds of veal that costs x  [#permalink]

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New post Updated on: 24 Feb 2017, 23:01
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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) (2x + 5y)/xy
(C) 5(2x + 5y)
(D) x + y
(E) (2x + 5y)/7

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Originally posted by SajjadAhmad on 22 Feb 2017, 02:32.
Last edited by Bunuel on 24 Feb 2017, 23:01, edited 1 time in total.
Edited the OA.
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Re: If a mixture of ground meat consists of 2 pounds of veal that costs x  [#permalink]

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New post 22 Feb 2017, 02:42
veal = 2lb of $x/lb = $2x;
beef = 5lb of $y/lb = $5y;

Total cost = $(2x+5y)
Total weight = 2 + 5 = 7lb
Cost per lb = $(2x+5y)/7

IMO Answer E.

I think OA A is incorrect.
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Re: If a mixture of ground meat consists of 2 pounds of veal that costs x  [#permalink]

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New post 22 Feb 2017, 04:31
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SajjadAhmad 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) (2x + 5y)/xy
(C) 5(2x + 5y)
(D) x + y
(E) (2x + 5y)/7



Since the options have variables, you can plug in some values to get the answer. The values that come immediately to mind are x = 1 and y = 1 i.e. if the cost of both meats is $1 per pound, the cost of the mix would be $1 per pound too.
We see immediately that only (E) gives 1 so it will be the answer.

Or just use the weighted average formula

Cavg = (C1*w1 + C2*w2)/(w1 + w2) = (x * 2 + y * 5)/(2 + 5) = (2x + 5y)/7

Answer (E)
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Re: If a mixture of ground meat consists of 2 pounds of veal that costs x  [#permalink]

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New post 22 Feb 2017, 19:47
1
Hi SajjadAhmad,

This question can be solved by TESTing VALUES.

IF...
X = 3
Y = 2
Then the total cost of the mixture is (2)($3) + 5($2) = $16 for 7 pounds. Thus, the average price per pound would be 16/7. Since we know that we're looking for a FRACTION with a 7 in the denominator, the correct answer really 'stands out.'

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Re: If a mixture of ground meat consists of 2 pounds of veal that costs x  [#permalink]

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New post 24 Feb 2017, 10:21
1
Answer is E.
BTW, can OA be wrong?
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Re: If a mixture of ground meat consists of 2 pounds of veal that costs x  [#permalink]

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New post 24 Feb 2017, 23:02
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Re: If a mixture of ground meat consists of 2 pounds of veal that costs x  [#permalink]

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New post 20 Mar 2018, 15:53
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SajjadAhmad 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 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

Answer: E

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Re: If a mixture of ground meat consists of 2 pounds of veal that costs x &nbs [#permalink] 20 Mar 2018, 15:53
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