Question

Please help me I really need it :( (-->WILL MARK BRAINLIEST<-- I ALREADY HAVE THE ANSWER FOR PART A, I JUST NEED PART B ANSWERED AND CAN YOU PLEASE EXPLAIN HOW YOU GOT YOUR ANSWER Thx :D)
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.


(a) What is the system that models this situation?


(b) Which of the following is a solution to the system: 2 lb peanuts and 3 lb mixture (2,3) ; 2.5 lb peanuts and 2.5 lb mixture (2.5, 2.5); 4 lb peanuts and 1 lb mixture (4,1) ? Show your work.  Please help me :'(

Answer 1

Answer:

(a) $\left\{\begin{array}{l}0.8m=2\\p+0.2m=3\end{array}\right.$

(b) correct choice is 2.5 lb peanuts and 2.5 lb mixture (2.5, 2.5);

Step-by-step explanation:

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.

1. In m pounds of the 80% almond-20% peanut mixture there are 0.8m pounds of almonds and 0.2m pounds of peanuts.

2. When added p pounds of peanuts to m pounds of mixture, you get (p+0.2m) pounds of peanuts and 0.8m pounds of almonds.

3. In 5 pounds of the 40% almond-60% peanut mixture there are $0.6\cdot 5=3$ pounds of peanut and $0.4\cdot 5=2$ pounds of almonds.

(a) Then you get a system of two equations:

$\left\{\begin{array}{l}0.8m=2\\p+0.2m=3\end{array}\right.$

(b) Solve this system. From the first equation

$m=\dfrac{2}{0.8}=2.5\ pounds,$

then

$p+0.2\cdot 2.5=3,\\ \\p=3-0.5,\\ \\p=2.5\ pounds.$