Chapter 11.1, Problem 59AYU

Mixing Nuts 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 selling the nuts separately?

To determine

To find: 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 selling the nuts separately?

Answer to Problem 59AYU

There must be $22.5$ pounds of cashews mixed with the 30 pounds of peanuts.

Explanation of Solution

Given:

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.

Calculation:

Let pounds of cashews be $x$, then the total pounds will be $x+30$.

$30\left(1.50\right)+x\left(5.00\right)=\left(30+x\right)\left(300\right)$   -----1

$45+5x=3x+90$

$2x=45$

$x=22.5$

Therefore, there must be $22.5$ pounds of cashews mixed with the 30 pounds of peanuts.