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If 3 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

If 3 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?

if x is the cost per pound of Apricots then 3 pounds cost = 3x If y is the cost per pound of prunes then 2 pounds cost =2y

So the total cost is 3x+2y for the 5 pounds So per pound cost will be = (3x+2y)/5

Answer A

Isn't this also a weighted average problem?

Yes, 'cost per pound of the mixture' is the 'weighted average cost'. You are essentially using the formula Cavg = (C1*w1 + C2*w2)/(w1 + w2)
_________________

This question can be solved in a variety of ways. If you catch the fact that there are only 5 total pounds of fruit, then you can avoid most of the work altogether, since the question asks for the average price per POUND of fruit.

Since none of the other explanations have TESTed VALUES, I'll show you how to use that approach here:

We have... 3 pounds of dried apricots that cost $X per pound and... 2 pounds of prunes that cost $Y per pound.

IF... X = 3 Y = 4

Then the apricots cost 3($3) = $9 and the prunes cost 2($4) = $8

Total cost = $17 and total weight = 5 pounds, so the correct answer will be 17/5

Answer A: (9+8)/5 = 17/5 This IS a match. Answer B: (9+8)/(3+4) = 17/7 NOT a match Answer C: (9+8)/(3)(4) = 17/12 NOT a match Answer D: 5(9+8) = 85 NOT a match Answer E: 9 + 8 = 17 NOT a match

If 3 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?

We can create the following weighted average equation:

(3x + 2y)/(3 + 2) = (3x + 2y)/5

Alternate Solution:

We add 3 pounds at x dollars per pound to 2 pounds at y dollars per pound to yield 5 pounds at z dollars per pound. We set up the following equation and solve for z:

3x + 2y = 5z

(3x + 2y)/5 = z

Answer: A
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

If 3 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Total cost for 5 pounds =3x+2y. Cost per pound of the mixture = 3x+2y/5.