SOLUTION: 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 poun
Question 1112609: 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 would selling the nuts separately?
Thank you so much!! Answer by ikleyn(52794) (Show Source):
Let x = "How many pounds of cashews should be mixed with the peanuts", in pounds.
This amount of cashew costs 5x dollars.
At the same time, 30 pounds of peanuts cost 1.50*30 = 45 dollars.
The two input ingredient cost 5x + 1.5*30 dollras, in total.
The store wants it would cost 3*(x+30) dollars.
So, your equation is
5x + 1.5*30 = 3*(x+30).
Simplify and solve it:
5x + 45 = 3x + 90
5x - 3x = 90 - 45 ====> 2x = 45 ====> x = = 22.5.
Answer. 22.5 pounds of cashews should be mixed with the peanuts.
Check. 5*22.5 + 1.50*30 = 157.50 dollars.
3*(22.5+30) = 157.50 dollars. ! Same value. Correct !
