Problem
A store sells cashews for $\$ 10.00$ per pound and peanuts for $\$ 0.50$ per pound. The manager decides to mix 29 pounds of peanuts with some cashews and sell th mixture for $\$ 6.00$ 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? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There should be $\square$ pounds of cashews in the mixture. (Type an integer or a decimal.) B. There are no mixtures that satisfy the given conditions
Solution
Step 1 ：Let the amount of cashews to be mixed be denoted as \(x\) pounds.
Step 2 ：The revenue from selling the nuts separately is \(10x + 0.5*29 = 10x + 14.5\).
Step 3 ：The revenue from selling the mixture is \(6(x + 29)\).
Step 4 ：According to the problem, these two amounts should be equal, so we can set up the following equation: \(10x + 14.5 = 6x + 174\).
Step 5 ：Solving this equation for \(x\) gives: \(10x - 6x = 174 - 14.5\), \(4x = 159.5\), \(x = 159.5 / 4\), \(x = 39.875\).
Step 6 ：\(\boxed{x = 39.875}\) pounds of cashews should be mixed with the peanuts.
