A manager bought 12 pounds of peanuts for $30. He wants to mix $5 per pound cashews with the peanuts to get a batch of mixed nuts that is worth $4 per pound. How many pounds of cashews are made?
look at the value of the nuts separately and together:
30 + 5(x) = 4(12+x)
30 + 5x = 48 + 4x
x = 18
To solve this problem, we can set up a system of equations. Let's denote the number of pounds of cashews as 'x'.
Since the manager wants to mix $5 per pound cashews with the peanuts to get a batch of mixed nuts worth $4 per pound, we can set up the following equation based on the value of the mixture:
(12 + x) pounds of mixed nuts * $4 per pound = $30 + $5x
Simplifying the equation, we have:
4(12 + x) = 30 + 5x
Now, let's solve for 'x':
48 + 4x = 30 + 5x
48 - 30 = 5x - 4x
18 = x
Therefore, the manager needs to mix 18 pounds of cashews with the peanuts to obtain a batch of mixed nuts worth $4 per pound.