How many pounds of peanuts costing $1.90/Ib and raisins costing $2.50/Ib should Mr. Bruckner mix to make 12 Ib of a trail mix that costs $2.05/ib

Let p and r be the amount of peanuts and raisins respectively.

p+r=12, p=12-r

We are given that:

(1.9p+2.5r) / 12=2.05, using p found above in this equation:

(1.9 (12-r) + 2.5r) / 12=2.05 perform indicated multiplication on left side

(22.8-1.9r+2.5r) / 12=2.05 combine like terms on left side

(22.8+0.6r) / 12=2.05 multiply both sides by 12

22.8+0.6r=24.6 subtract 22.8 from both sides

0.6r=1.8 divide both sides by 0.6

r=3, and since p=12-r

p=12-3

p=9

So Mr. Bruckner will need to mix 9 pounds of peanuts with 3 pounds of raisins to make a 12 pound mixture which costs $2.05 per pound.