+11 Delaney would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture.
What is the system that models this situation?
Which of the following is a solution to the system: 2 lb peanuts and 3 lb mixture; 2.5 lb peanuts and 2.5 lb mixture; 4 lb peanuts and 1 lb mixture? Show your work.
Answer:
First of all p + m = 5 because there is a total of 5 pounds of mixture to be made. Now for there to be 40% of almonds there must be 0.4*5 = 2 pounds almonds So as there are 80% almonds in the mixture the amount of m must be 2 / 0.8 = 2.5 pounds so we have p + 2.5 = 5 so p = 2.5 Answer is 2.5 pounds of peanuts and 2.5 pounds of the mixture.
