Pretzels cost 3 per pound dried fruit 5 per pound and nuts 8

Pretzels cost $3 per pound, dried fruit $5 per pound, and nuts $8 per pound. How many pounds each should be used to produce 200 pounds of trail mix costing $6 per pound in which there are twice as many pretzels (by weight) as dried fruit? Show equations and augmented matrix. Round answers to the nearest .01 pound.

Solution

let x=pounds of pretzels, y=pounds of dried fruit and z=pounds of nuts

Simply based on weight, we want the sum to be 200 pounds:

x + y + z = 200

Now, for cost, we want the following equation to hold, based on the price of each item, including the trailmix itself:

($3/lb)x+ ($5/lb)y + ($8/lb)z = 140($6/lb)

Also, since we know there are twice as many pretzels(by weight) as dried fruit:

x = 2y

We can take x = 2y and sub it into the second equation. Thus:

(2y) + y + z =200

We subtract 3y from each side and get:

z = 200 - 3y

Now, since we have z and x in terms of y, we substitute everything into the first equation:

3(2y) + 5(y) + 8(200 - 3y) = 200(6)
6y + 5y +8(200) - 24y = 200(6)
-13y= -2(200)

Divide by -13:

y = 30.76

Now plug that back into the other equations for z and x in terms of y:

x=2(y) = 2(30.76) = 61.52

z=200 - (3y) = 200 - 3*30.76 = 107.72

Hope this will helpful. Thanks and God bless you:)