Angelina spend $50 on 16 packages of cookies for her club members. sugar cookies cost $2.50 per package and chocolate chip cookies cost $3.50 per package. how many packages of each cookie does Angelina buy?

6 packs of sugar cookies and 10 packs of chocolate chip cookies.

Step-by-step explanation:

Let the quantity of sugar cookies be x packs and the quantity of chocolate chip cookies be y packs. Total packs are 16. Therefore: x + y = 16. This implies y = 16 - x (Equation 1).

It is given that a pack of sugar cookies is priced at $2.5 and a pack of chocolate chip cookies is priced at $3.5. It is also given that the student spends a total of $50 on the cookies. Since x packs of sugar cookies and y packs of chocolate chip cookies are to be bought, therefore:

2.5x + 3.5y = 50 (Equation 2).

Put equation 1 in equation 2.

2.5x + 3.5 (16 - x) = 50.

2.5x + 56 - 3.5x = 50.

-x = - 6.

x = 6.

Put x = 6 in equation 1.

y = 16 - 6.

y = 10.

Therefore, Angelina will buy 6 packs of sugar cookies and 10 packs of chocolate chip cookies!