Delaney would like to make a 10 lb nut mixture that is 60% peanuts and 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.(a) What is the system that models this solution?(b) Which of the following is a solution to the system: 4 lb peanuts and 6 lb mixture; 5 lb peanuts and 5 lb mixture; 8 lb peanuts and 2 lb mixture? Show your work.

Answer:If there is "p" pounds of peanuts and "m" pounds of '20% peanuts and 80% almonds' mixture, then, we can get the following equations,p + m = 10 -----------(1) and4m/5 = 4 ------------(2)whose solution is 5 lb peanuts and 5 lb mixture.Step-by-step explanation:In the mixture which Delaney wants to make there would be[tex]\frac {10 \times 60}{100}[/tex] lb = 6 lb of peanutsSo, there will be (10 - 6) lb  = 4 lb of almondsIf  Delaney has "p" pounds of peanuts and "m" pounds of the '20% peanuts and 80% almonds' mixture, then according to the question,p + m = 10 -----------(1) and4m/5 = 4 ------------(2)So, from (2), m = 5 --------------(3)So, from (1) and (3) , p = (10 - 5) = 5