Question

Dani bought a total of $8$ pounds of peanuts and cashews.

Peanuts, $\mathrm{p}$, cost $\$2$ per pound and the cashews, $\mathrm{c}$, cost $\$5$ per pound.

The total amount Dani spent on the peanuts and cashews was $\$25$.

Which system of equations could be solved to find how many pounds of peanuts Dani bought $?$

• A. $$\begin{gathered} 2\mathrm{p}+5\mathrm{c}=25 \\ \mathrm{p}+\mathrm{c}=8 \end{gathered}$$
• B. $$\begin{gathered} 5\mathrm{p}+2\mathrm{c}=25 \\ \mathrm{p}+\mathrm{c}=8 \end{gathered}$$
• C. $$\begin{gathered} 2\mathrm{p}+5\mathrm{c}=8 \\ \mathrm{p}+\mathrm{c}=25 \end{gathered}$$
• D. $$\begin{gathered} 2\mathrm{p}=8 \\ 5\mathrm{c}=25 \end{gathered}$$

Answer 1

The correct option is A

$$\begin{gathered} 2\mathrm{p}+5\mathrm{c}=25 \\ \mathrm{p}+\mathrm{c}=8 \end{gathered}$$

Find the system of equations to find how many pounds of peanuts Dina bought:

Explanation for correct option:

Option $\mathbf{\left(}\mathbf{A}\mathbf{\right)}$:

Let the weight of peanuts be $\mathrm{p}$ pounds and the weight of cashews be $\mathrm{c}$ pounds.

Since the total weight of peanuts and cashews was $8$, it follows that:

$\mathbf{p}\mathbf{+}\mathbf{c}\mathbf{=}\mathbf{8}$

Cost of $1$ pound of peanuts was $\$2$

So, the cost of $\mathrm{p}$ pounds of pea will be $\$2\mathrm{p}$.

Cost of $1$ pound of cashews was $\$5$

So, the cost of $\mathrm{c}$ pounds of cashews will be $\$5\mathrm{c}$.

Since the total cost of the peanuts and the cashews was $\$25$, it follows that:

$\mathbf{2}\mathbf{p}\mathbf{+}\mathbf{5}\mathbf{c}\mathbf{=}\mathbf{25}$

Hence, the system of equations are as follows:

$\mathbf{p}\mathbf{+}\mathbf{c}\mathbf{=}\mathbf{8}$

$\mathbf{2}\mathbf{p}\mathbf{+}\mathbf{5}\mathbf{c}\mathbf{=}\mathbf{25}$

Explanation for incorrect option:

Since the system of equations given above, not equivalent to option $\left(\mathrm{B}\right)$, so option $\left(\mathrm{B}\right)$ is incorrect.

Since the system of equations given above, not equivalent to option $\left(\mathrm{C}\right)$, so option $\left(\mathrm{C}\right)$ is incorrect.

Since the system of equations given above, not equivalent to option $\left(\mathrm{D}\right)$, so option $\left(\mathrm{D}\right)$ is incorrect.

Hence, the only correct option is $\mathbf{\left(}\mathbf{A}\mathbf{\right)}$.