Question

Santa's elves are selling

Answer 1

cost of one peppermint cookies = $ 0.6

cost of one cinnamon sugar cookies = $ 0.3

Solution:

Let "p" be the cost of one peppermint cookies

Let "c" be the cost of one cinnamon sugar cookies

To find: cost of each cookie

On  the first day, they sold 120  peppermint cookies and 30  cinnamon sugar cookies for a  total of $81

We can frame a equation as:

120  peppermint cookies x cost of one peppermint cookies + 30  cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 81

$120 \times p + 30 \times c = 81$

120p + 30c = 81  --------- eqn 1

The next day  they made $60 by selling 70  peppermint cookies and 60  cinnamon sugar cookies

70  peppermint cookies x cost of one peppermint cookies + 60  cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 60

$70 \times p + 60 \times c = 60$

70p + 60c = 60 --------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "p" and "c"

Multiply eqn 1 by 2

240p + 60c = 162  --- eqn 3

Subtract eqn 2 from eqn 3

240p + 60c = 162

70p + 60c = 60

(-) -------------------------

170p = 102

p = 0.6

Substitute p = 0.6 in eqn 1

120p + 30c = 81

120(0.6) + 30c = 81

72 + 30c = 81

30c = 9

c = 0.3

Summarizing the results:

cost of one peppermint cookies = $ 0.6

cost of one cinnamon sugar cookies = $ 0.3