Read the problem and identify what you are looking for. You are looking for the number of pounds of peanuts and the number of pounds of cashews Greta needs to use to make her nut mix and stay within her budget constraints. Name what you are looking for. Let $p$ represent the number of pounds of peanuts and let $c$ represent the number of pounds of cashews she needs to use. It may help to use a table, similar to the one used in Example 5.4.28 to help organize your information. Then, place the $p$ and $c$ under the number of pounds for the types peanuts and cashews. For the type nut mix, place $5$ since that is the total number of pounds of nut mix that she needs to make. Also place the price per pound for each type, including the total allowed in her budget for the nut mix, in the Value column. Then, the values for the last column are obtained by multiplying the number of pounds times the value for each type. Translate into a system of equations. Your two equations will come from the Number of Pounds column and the Total Value column, giving you the following system: $$\begin{gathered} \begin{cases} p+c=5 \\ 4p+9c=30 \end{cases} \end{gathered}$$ Solve the system of equations. We will use elimination. Multiply the first equation by $-4$ to eliminate $p\text{.}$ $$\begin{gathered} \multiplyleft{-4}(p+c)=\multiplyleft{-4}(5)\\ 4p+9c=30 \end{gathered}$$ Simplify and add. Then solve for c. $$\begin{aligned} \begin{aligned}-4p-4c\\{}+4p+9c\end{aligned}\amp=\begin{aligned}-20\\{}+30\end{aligned} \end{aligned}$$ So we have $$\begin{gathered} 5c=10\\ c=2 \end{gathered}$$ To find the number of pounds of poeanuts, substitute $c=2$ into the first equation, then solve for $p\text{.}$ $$\begin{gathered} p+c=5\\ p+\substitute{2}=5\\ p=3 \end{gathered}$$ Answer the question. Greta should mix $3$ pounds of peanuts with $2$ pounds of cashews to create the nut mix. The check is left to the reader.