Question

How many pounds of nuts selling for $6 per pound and pounds of raisins selling for $3 per pound should Kurt combine to obtain 120 pounds of trail mix that cost him $5 per pound?

Answer 1

80 pounds of nut sold and 40 pounds of raisins sold.

Explanation:

Let x be the number of pounds of nut sold and y be the number of pounds of raisins sold.

Combine weight of trail mix is 120 pounds.

`x+y=120` .... (1)

Nuts selling for $6 per pound and pounds of raisins selling for $3 per pound. The cost of trail mix is $5 per pound.

`6x+3y=5* 120`

`6x+3y=600`

Divide both sides by 3.

`2x+y=200` ..... (2)

Subtract equation (1) from equation (2).

`2x+y-(x+y)=200-120`

`2x+y-x-y=80`

`x=80`

The value of x is 80.

Put this value in equation (1).

`80+y=120`

Subtract 80 from both sides.

`80+y-80=120-80`

`y=40`

The value of y is 40.

Therefore, 80 pounds of nut sold and 40 pounds of raisins sold.