Question

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 40 pounds of? peanuts, the manager decided to mix the 40 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?

Answer 1

To ensure no change in profit, the manager should mix 320 pounds of cashews with the peanuts.

Step-by-step explanation:

To ensure no change in profit, the manager needs to determine the cost price per pound of peanuts. Since the mixture is being sold for $2.00 per pound, the cost price per pound of peanuts can be calculated by subtracting the selling price per pound of cashews from the selling price of the mixture:

Cost price per pound of peanuts = Selling price per pound of mixture - Selling price per pound of cashews = $2.00 - $1.50 = $0.50

Therefore, the cost price per pound of peanuts is $0.50. To find out the amount of cashews needed to be mixed with the peanuts, we can set up a ratio using the cost price of peanuts and cashews:

Cashews : Peanuts = $4.00 : $0.50 = 8 : 1

Since we want to mix 40 pounds of peanuts, we can calculate the amount of cashews needed:

Amount of cashews = 40 pounds of peanuts × (8/1) = 320 pounds

Therefore, the manager should mix 320 pounds of cashews with the peanuts to ensure no change in profit.

Answer 2

10 lbs

Step-by-step explanation:

Let c represent the number of pounds of cashews to be added. Then the total cost of the mix will be ...

4.00c +1.5(40) = 2.00(c+40)

4c +60 = 2c +80 . . . . . . . . . . . simplify

2c = 20 . . . . . . . . . . . . . . . . . . . subtract 60 + 2c

c = 10 . . . . . . . . . . . . . . . . . . . . .divide by 2

10 pounds of cashews should be mixed with the peanuts.