Question

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

Answer 1

Answer:

8 pounds of peanuts, 6 pounds of raisins and 6 pounds of chocolate chips

Step-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 cost

2x+2.50y+4y=20·2.75.

Solve the system of two equations:

$\left \{ {{x+2y=20} \\ \\ \\ \\ \\ \\ \atop {2x+6.5y=55}} \right.$

From the first equation:

$x=20-2y$

Substitute x into the second equation:

$2(20-2y)+6.5y=55\\ \\40-4y+6.5y=55\\ \\2.5y=15\\ \\25y=150\\ \\y=6\\ \\x=20-2\cdot 6=8$