Delaney would like to make a 10 lb nut mixture that is 60% peanuts and and 40% almonds. She has several pounds of peanuts and se

Question

9 days ago

6

Delaney would like to make a 10 lb nut mixture that is 60% peanuts and and 40% almonds. She has several pounds of peanuts and se

veral 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 solution?
(b) Which of the following is a solution to the system: 4 lb peanuts and 6 lb mixture; 5 lb peanuts and 5 lb mixture; 8 lb peanuts and 2 lb mixture? Show your work.

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-04-07T07:32:37+03:00

Response:

If there are "p" pounds of peanuts and "m" pounds of a mixture containing '20% peanuts and 80% almonds', then we can formulate the following equations:

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

The solution yields 5 lb peanuts and 5 lb mixture.

Detailed explanation:

In the mixture that Delaney desires to create, there will be

$\frac {10 \times 60}{100}$ lb

= 6 lb of peanuts

Thus, there will be (10 - 6) lb

= 4 lb of almonds

If Delaney has "p" pounds of peanuts and "m" pounds of the '20% peanuts and 80% almonds' mixture, then based on the problem statement,

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

From equation (2), we derive

m = 5 --------------(3)

From (1) and (3), we find that

p = (10 - 5) = 5