Question

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; 2.5 lb peanuts and
2.5 lb mixture; 4 lb peanuts and 1 lb mixture? Show your work

Answer 1

Answer:

Step-by-step explanation:

Let a be peanuts and b be almonds .

Now,

4a+5b=44--->1×1

2a+4b=31---->2×2

Solving 1 and 2,

4a+5b=44

4a+8b=62

-_________

-3b=18

b= - 18/3

b=-6

Now, replacing in any equation .

2a+4b=31

2a+4(-6)=31

2a-24=31

2a=55

a=55/2

a=22.5

Verification :-

2(55/2)+4(-6)=31

55-24=31

31=31

Thank you