# Cashews at $7.40 a pound are mixed with peanuts at$2.60 a pound. If there are 18 pounds in the mixture and the mixture sells for $5.80 per pound, how many pounds of cashews are there in the mixture? ##### 1 Answer Aug 16, 2015 I found: $12$pounds of cashews $6$pounds peanuts #### Explanation: Call $C$and $P$the quantities of the two; you have: $\left\{\begin{matrix}C + P = 18 \\ 7.4 C + 2.6 P = 5.8 \cdot 18 = 104.4\end{matrix}\right.$solve the system (by substitution, for example) to get: $C = 18 - P$$7.4 \left(18 - P\right) + 2.6 P = 104.4$So: $P = 6$pounds $C = 12\$ pounds

This answers assumes a seller that sells at a price exactly according to the mixture. Many sellers are would be fully willing to sell you a "mixture" that is completely peanuts for them to have a profit. Assuming a seller would not sell for a loss, the answer would be "AT LEAST 6 pounds of peanuts, and AT MOST 12 pounds of cashews".