Afood store makes a 11-lb mixture of peanuts, almonds, and raisins. the cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. the mixture calls for twice as many peanuts as almonds. the total cost of the mixture is $21.00. how much of each ingredient did the store use?

So, let's say, "p" is how many lbs of peanuts, "a" of almonds and "r" of raisins



so.... whatever p,a,r are, they will sum up to 11, thus
p+a+r = 11

and whatever 1.5p+3a+1.5r is, must add up to 21

1.5p+3a+1.5r = 21

now.. .we know that the mixture uses twice as many peanuts as almonds, namely, if there's "a" amount of almonds, then of peanuts is twice that much or 2*a, or 2a, thus p = 2a

thus    

solve for "a" to see how many lbs of almonds will be needed

what about raisins?  well, r = 11 - 3a
and peanuts?   well, p = 2a