Solve the problem using a system of equations.
-A company sells nuts in bulk quantities. When bought in bulk, peanuts sell for $\$ 1.20$ per pound, almonds for $\$ 2.35$ per pound, and cashews for $\$ 3.30$ per pound. Suppose a specialty shop wants a mixture of 210 pounds that will cost $\$ 2.42$ per pound. Find the number of pounds of each type of nut if the sum of the number of pounds of almonds and cashews is twice the number of pounds of peanuts. Round your answers to the nearest pound.
A) Peanuts: $70 \mathrm{lb}$., almonds: $40 \mathrm{lb}$., cashews: $100 \mathrm{lb}$.
B) Peanuts: $40 \mathrm{lb}$., almonds: $100 \mathrm{lb}$., cashews: $70 \mathrm{lb}$.
C) Peanuts: $80 \mathrm{lb}$., almonds: $40 \mathrm{lb} .$, cashews: $90 \mathrm{lb}$.
D) Peanuts: $100 \mathrm{lb}$., almonds: 70 lb., cashews: $40 \mathrm{lb}$.

Question

Quizplus · Accepted Answer

The system of equations based on the problem statement is: $1.20p + 2.35a + 3.30c = 2.42 \times 210$, $p + a + c = 210$, and $a + c = 2p$. Solving these equations gives the solution: peanuts: $70 \mathrm{lb}$, almonds: $40 \mathrm{lb}$, cashews: $100 \mathrm{lb}$.

Solve the Problem Using a System of Equations $1.20\$ 1.20$1.20 Per Pound, Almonds For

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