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?

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:

From the first equation:

Substitute x into the second equation:

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0