Algebra 2 World Problem

Question

Suppose you want to fill nine 1 pound tins with a snack mix. You have $15 and plan to buy almonds for $2.45 per pound, hazelnuts for $1.85 per pound, and raisins for $0.80 per pound. You want the mix to contain an equal amount of almonds and hazelnuts and twice as much of the nuts as raisins by weight. How many of each ingredient should you buy?

Answer 1

almonds =x= 5/3, hazel = y = 5/3, raisin = z= 10/3

x=y z =2x=2y

3 equations 3 unknowns

2.45x + 1.85y + .8z = 15

x=y

z =2x

solve by matrix algebra, substitution elimination, your choice

9 one lb tins means 5x/3 + 5y/3 + 10z/3 = 9

10x/3 +10z/3 = 9

10x/3 + 20x/3 = 9

30x/3 = 9

10x = 9

x = 9/10 = .9 lbs almonds = .9 lbs hazel and 1.8 lbs raisins to fill 9 tins each