Q. 59 - Precalculus Enhanced with Graphing Utilities

Question

A store sells cashews for \(5.00 per pound and

peanuts for \)1.50 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

Step-by-Step Solution

Answer

The amount of cashew required to mix with peanut is 22.5pounds

Step 1: Given information

A store sells cashews for $5.00 per pound and

peanuts for $1.50 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound.

Step 2 Find the equation and solve

Let x be the required weight of cashew to create the mixture

$$\begin{gathered} 3(x+30)=5\left(x\right)+1.5\left(30\right) \\ 3x+90=5x+45 \\ 2x=45 \\ x=22.5 \end{gathered}$$

Step 3: Conclusion

The amount of cashew required to mix with peanut is 22.5pounds