Sarah would like to make a 6lb nut mixture that is 60% peanuts and 40% almonds. she has several pounds of a mixture that is 80% peanuts and 20% almonds and several pounds of a mixture that is 50% peanuts and 50% almonds. a) what is the system that models this situation? b) what is the solution to the system? how many pounds of the 80/20 mixture? how many pounds of 50/50 mixture? show your work!

                 2 lbs of 80/20 and 4 lbs of 50/50 mixtures

Step-by-step explanation:

Let A represent the quantity of the 80/20 mixture.  Let B represent the quantity of the 50/50 mixture.

Let's solve based on peanuts:

First, set up the equations:

Now, solve the system above using substitution: A + B = 6  ⇒  B = 6 - A

0.8A + 0.5(6 - A) = 0.6(6)

0.8A + 3 - 0.5A = 3.6

           3 + 0.3A = 3.6

                 0.3A = 0.6

                       A = 2

Lastly, plug in A (above) into the Quantity equation to solve for B:

A + B = 6

(2) + B = 6

       B = 4

SIDE NOTE: You could have solved based on almonds by setting up the system as:

which would give the same answer (A = 2, B = 4)

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.