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.

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 1

Answer: The system that models this situation is:

{p+m=50.6p+0.2m=0.6×5​

This system can be solved by substitution or elimination. One possible solution is:

Multiply the second equation by 5 to eliminate the fractions:

{p+m=53p+m=15​

Subtract the first equation from the second equation to eliminate m:

2p=10

Solve for p:

p=210​=5

Substitute p into the first equation to find m:

m=5−p=5−5=0

The solution is (p, m) = (5, 0), which means Delaney needs 5 lb of peanuts and 0 lb of mixture.

Another possible solution is:

Multiply the first equation by -0.2 to eliminate m:

{−0.2p−0.2m=−10.6p+0.2m=3​

Add the two equations to eliminate m:

0.4p=2

Solve for p:

p=0.42​=5

Substitute p into the first equation to find m:

m=5−p=5−5=0

The solution is (p, m) = (5, 0), which means Delaney needs 5 lb of peanuts and 0 lb of mixture.

Therefore, the only correct option among the given choices is 4 lb peanuts and 1 lb mixture.