Question

a popular mixture of potpourri includes pine needles and lavender. If pine needles cost $1.50 per ounce and lavender cost $4 per ounce, how much of each ingredient should be mixed to make 80 oz of the potpourri that is worth $200

Answer 1

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: $x+y=80$ oz

Thus, $y=80-x$.....................................(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: $1.5x$.

Likewise, the total cost of lavender in the potpourri will be $4y$

From (Equation 1) we thus have, $4y=4(80-x)$

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

$1.5x+4(80-x)=200$

$1.5x+320-4x=200$

$-2.5x+320=200$

$-2.5x=200-320=-120$

Therefore,

$\therefore x=\frac{-120}{-2.5} =48$

Thus, from (Equation 1), $y=80-48=32$

Therefore, the amount of pine needle in the potpourri is 48 oz and the amount of lavender is 32 oz