A grocer wishes to mix three kinds of nuts to obtain $40$ pounds of a mixture priced at $\$4.45$ per pound. Peanuts cost $\$3$ per pound, almonds cost $\$5$ per pound, and pistachios cost $\$5.5$ per pound. Half of the mixture is composed of peanuts and almonds. How many pounds of $\text{ peanuts }$ should the grocer use?

A) $16$ pounds
B) $20$ pounds
C) $28$ pounds
D) $15$ pounds
E) $30$ pounds

The total cost of the 40-pound mixture is $40\times 4.45=178$ dollars. Since half of the mixture is peanuts and almonds, this means 20 pounds are a combination of these two nuts. Let $x$ be the pounds of peanuts and $20-x$ be the pounds of almonds. The cost equation for peanuts and almonds is $3x+5(20-x)$ . The remaining 20 pounds are pistachios, costing $20\times 5.5=110$ dollars. The equation for the total cost is $3x+5(20-x)+110=178$ . Solving for $x$ gives $x=16$ .