A nut store normally sells cashews for 400 per pound and pea

A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound. But at the end of the month the peanuts had not sold well, so, in order to sell 20 pounds of peanuts, the manager decided to mix the 20 pounds of peanuts with some cashews and sell the mixture for $2.00 per pound. How many pounds of cashews should be mixed with the peanuts to ensure no change in the profit? The manager should mix pounds of cashews with the peanuts.

Solution

let x be the number of pounds of cashews to be mixed.

If sold individually, Total price will be 20* 1.5 + x*4 = 30+4x

After mixing we have (20 + x) *2 = 40+2x

Since no change in profit, 40 +2x = 30 +4x

x= 5

So manager should mix 5 pounds of cashews with 20 pounds of peanuts