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.