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

Question

Quizplus · Accepted Answer

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 $x = 16$.

A Grocer Wishes to Mix Three Kinds of Nuts to Obtain