Suppose the leader of a camping trip is putting together a trail mixraisins, and chocolate chips. The mix is to consist of equal parts raisins and chocolate. Ifpeanuts cost $2/lb, raisins cost $2.50/lb, and chocolate chips cost $4/lb, how much of eachshould be mixed to create 20 lbs of trail mix that costs $2.75/lb?

Answer:8 pounds of peanuts, 6 pounds of raisins and 6 pounds of chocolate chipsStep-by-step explanation:Let x be the number of pounds of peanuts and y be the number of pounds of raisins and chocolate chips.Peanuts cost $2 per pound, then x pounds cost $2x.Raisins cost $2.50 per pound, then y pounds cost $2.50y.Chocolate chips cost $4 per pound, then y pounds cost $4y.In total, x+y+y=20 and those 20 pounds cost2x+2.50y+4y=20·2.75.Solve the system of two equations:[tex]\left \{ {{x+2y=20} \\ \\ \\ \\ \\ \\ \atop {2x+6.5y=55}} \right.[/tex]From the first equation:[tex]x=20-2y[/tex]Substitute x into the second equation:[tex]2(20-2y)+6.5y=55\\ \\40-4y+6.5y=55\\ \\2.5y=15\\ \\25y=150\\ \\y=6\\ \\x=20-2\cdot 6=8[/tex]