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A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?

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Question

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A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?



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anonymous · Answer

Let $c$ and $p$ denote the pounds of cashews and peanuts, respectively. Then you have the system
$$\begin{cases}
c+p=10&\text{because you want a 10 pound mix}\
4p+6.5c=4.75(c+p)&\text{because you want the mix's price to be }$4.75
\end{cases}$$
Solve for $c$. Should be easy by substitution.