Answer:
5 pounds
Step-by-step explanation:
Let x represent the pounds of cashews combined with 5 pounds of peanuts,
Thus, the total weight of the mixture (in pounds) equals x + 5,
∵ the overall cost of x pounds of cashew nuts plus the cost of 5 pounds of peanuts must equal the combined cost of the mixture,
Moreover, the cost of x pounds of cashews is $14 for each pound, while the cost for 5 pounds of peanuts is $6.50, and the overall combined cost for the mixed nuts is $10.25,
⇒ 14x + 5(6.5) = 10.25(x+5)
⇒ 14x + 32.5 = 10.25x + 51.25
⇒ 14x + 32.5 - 10.25x = 51.25
⇒ 3.75x = 51.25 - 32.5
⇒ 3.75x = 18.75
⇒ x = 5
Consequently, 5 pounds of cashews would be necessary for the mix.