giving 100 pts/ brainliest!! please help this is due in 20 minutes

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.

We need to change that 80% of almond into 40%, by adding more peanuts. To do this, we must add the same weight of peanuts as there is in the 80-20 mixture, to halve the ratio of almonds.

Therefore, p=m

Because the total mixture is 5 lbs, and the 80-20 and peanut mixture are the same weight, we know that p=m=2.5 lbs

Step-by-step explanation:

Answer Link

sqdancefan sqdancefan · Answer 2 · 2023-01-07T00:38:18+01:00

Answer:

p + m = 5, p + 0.2m = 0.6(5)
2.5 lb peanuts; 2.5 lb almond mix

Step-by-step explanation:

You have peanuts and an 80-20 almond-peanut mix, and you want to know how many pound of each are needed for 5 lb of a 60% peanut mix.

System of equations

The system of equations relating the pounds of peanuts (p) and the pounds of almond mix (m) will describe the total mixture weight, and the weight of the peanuts.

p + m = 5 . . . . . . total mixture weight is 5 lb

p + 0.20m = 0.60(5) . . . . . weight of peanuts in the 60% peanut mix

Solution

We can subtract the second equation from the first to eliminate the variable p:

(p +m) -(p +.2m) = (5) -(.6)(5)

0.8m = 0.4(5) . . . simplify

m = 2.5 . . . . . . . . divide by 0.8

p = 5 -m = 2.5

The solution to the system is 2.5 lb peanuts and 2.5 lb mixture.