Bunuel wrote:
Tough and Tricky questions: Mixture Problems.
A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?
A) 40
B) 45
C) 50
D) 55
E) 60
Kudos for a correct solution.Source: Chili Hot GMAT
A weighted average approach I use in mixture problems. Here, peanuts cost an "average" of $1.50 per pound. Cashews cost an average of $4.00 per pound.
\(Ave_{A}(Qty_{A}) + Ave_{B}(Qty_{B}) = Ave_{A+B}(Qty_{A+B})\)Where
\(Ave_{A+B}\) is the desired cost of the resultant mixture of nuts
Let P = # of pounds of peanuts at $1.50 a pound
Let C = # of pounds of cashews at $4.00 a pound
P + C = 100
P = 100 - C
1.50(P) + 4.00(C) = 2.50(P + C)*
1.5(100 - C) + 4(C) = 2.5(100)
150 - 1.5C + 4C = 250
2.5C = 100
C = \(\frac{100}{2.5}=\frac{1000}{25}= 40\)
Answer A
*We know that (P + C) = 100. I wrote it that way to parallel the equation.
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