A grocer wants to make a 10 -pound mixture of peanuts and cashews that he can sell for $$ \$ 475 $$ per pound. If peanuts cost $$ \$ 4.00 $$ per pound and cashews cost $$ \$ 6.50 $$ per pound, how many pounds of each should he use? Let $$ p= $$ pounds of peanuts and let $$ \mathrm{c}= $$ pounds of cashews. Write a system of equations that could be used to solve the problem WRITER

Question

UpStudy AI · Accepted Answer

To solve the problem, we need to set up a system of equations based on the information provided.

### Known Conditions:
1. The total weight of the mixture is 10 pounds.
2. The total value of the mixture is $$ 10 \times 475 = 4750 $$ dollars.
3. The cost of peanuts is $$ 4.00 $$ dollars per pound.
4. The cost of cashews is $$ 6.50 $$ dollars per pound.

### Variables:
- Let $$ p $$ = pounds of peanuts
- Let $$ c $$ = pounds of cashews

### Step 1: Set up the equations

1. **Total weight equation**: The total weight of peanuts and cashews must equal 10 pounds.
   $$
   p + c = 10
   $$

2. **Total value equation**: The total value of the peanuts and cashews must equal $$ 4750 $$ dollars.
   $$
   4p + 6.5c = 4750
   $$

### System of Equations:
The system of equations that can be used to solve the problem is:
$$
\begin{align*}
1. & \quad p + c = 10 \
2. & \quad 4p + 6.5c = 4750
\end{align*}
$$

This system can now be solved to find the values of $$ p $$ and $$ c $$.
The system of equations to solve the problem is: $$ \begin{align*} 1. & \quad p + c = 10 \ 2. & \quad 4p + 6.5c = 4750 \end{align*} $$

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions