Ineed
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i know it looks like a lot but it is not : )

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% almond20% peanut mixture.

(e) identify two relationships, setup an equation for each relationship, and use those two equations to setup a
system that models this situation.

(f) use the system you found from part a to determine which of the following is a solution to the system:

a. 2 lb peanuts and 3 lb mixture
b. 2.5 lb peanuts and 2.5 lb mixture
c. 4 lb peanuts and 1 lb mixture
note: make sure to show your work verifying if the answer is a solution to the system.

This is a mixture problem. Let's call the mixture of

20%peanuts - 80% almonds as mixture A

Let's call the

100% peanuts as mixture B

and the

60% peanuts - 40% almonds as mixture C

Since we get mixture C by adding mixture A and B together, we know that the amount in pounds of mixture A and mixture B is 5 pounds.

Hence we

let m be the amount in pounds of 20%peanuts-80% almonds mixture, or mixture A

and

50-m be the amount in pounds of mixture B

So, the system of equations that models this situation is:

0.20m + 1(50-m) = 0.60(5)

0.80m + 0(50-m) = 0.40(5)

Solving for m using equation 2 gives us

m = 2.5 lb.

That means it will take 2.5 lb of mixture A (20%peanuts-80%almonds) and 2.5 lb of mixture B (100%peanuts) to form 5 lb of mixture C (60%peanuts-40%almonds).

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Step-by-step explanation: Look it up it makes things a lot eaiser

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