Respuesta :
Let the amount of pine needle in the potpourri be x oz.
Let the amount of lavender in the potpourri be y oz.
Then, from the given question it is clear that: [tex] x+y=80 [/tex] oz
Thus, [tex] y=80-x [/tex].....................................(Equation 1)
Now, if the cost of pine needle is $1.5/ounce then, the total cost of pine needle in the potpourri will be: [tex] 1.5x [/tex].
Likewise, the total cost of lavender in the potpourri will be [tex] 4y [/tex]
From (Equation 1) we thus have, [tex] 4y=4(80-x)[/tex]
Since the total cost of the 80 oz potpourri is $200, therefore, the above information can be combined to yield:
(total cost of pine needle in the potpourri)+(total cost of lavender in the potpourri)=total cost of the potpourri
[tex] 1.5x+4(80-x)=200 [/tex]
[tex] 1.5x+320-4x=200 [/tex]
[tex] -2.5x+320=200 [/tex]
[tex] -2.5x=200-320=-120 [/tex]
Therefore,
[tex] \therefore x=\frac{-120}{-2.5} =48 [/tex]
Thus, from (Equation 1), [tex] y=80-48=32 [/tex]
Therefore, the amount of pine needle in the potpourri is 48 oz and the amount of lavender is 32 oz
