A bin in a nut store contains 100 lb of amixture of almonds, peanuts, and raisins. Almonds sell for $1.89/lb, peanuts for $1.58/lb, and raisins for $1.39/lb. If the mixture contains twice as many pounds of peanuts as almonds, and if the total value of the almonds and the raisins in the mixture is $93.40, how many pounds of each item does the mixture contain?

A + P + R = 100lbs

A + 2A = 100 – R which is the same thing as 3A – 100 = –R

Also,

1.89A + 1.39R = 93.40 which is the same thing as 1.89A – 93.40 = –1.39R

We now have 2 equations….
3A – 100 = –R
1.89A – 93.40 = –1.39R

We must make the R equal on both. So we must multiply equation 1, 3A – 100 = –R, by 1.39

Now we have…..
4.17A – 139 = –1.39R
1.89A – 93.40 = –1.39R

Now we combines the 2 equations….
4.17A – 139 = 1.89A – 93.40
2.28A = 45.6
A = 20

Therefore, there are 20lbs of Almonds.
There are twice as many Peanuts as Almonds, so there are 40lbs of Peanuts.
That leaves 40lbs (100-20-40) of Raisins

FINAL ANSWER:
Almonds = 20lbs
Peanuts = 40lbs
Raisins = 40lbs