Question

A snack food is made by mixing 3 lb of popcorn that costs $0.80 per pound with caramel that costs $2.20 per pound. How much caramel is needed to make a mixture that costs $1.60 per pound?

Answer 1

Assuming you retain the same number of pounds of popcorn (3)

find cost now
3*0.80=2.40
2.20 per pound
(2.4+2.2x)/(3+x)=1.6
times 3x both sides
2.4+2.2x=4.8+1.6x
minus 1.6x from both sides
2.4+0.6x=4.8
minus 2.4 both sides
0.6x=2.4
divide both sides by 0.6
x=4

4 pounds of caramel are needed