Question

Santa's elves are selling

cookies for a bale sale. On
the first day, they sold 120
peppermint cookies and 30
cinnamon sugar cookies for a
total of $81. The next day
they made $60 by selling 70
peppermint cookies and 60
cinnamon sugar cookies.
Find the cost of each cookie.​

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 * p + 30 * 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 * p + 60 * 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