Mrs. Julien’s and Mrs. Castillejo’s classes are selling cookie dough for a school fundraiser. Customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. Mrs. Julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. Mrs. Castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) Write the system of equations that model the problem. Be sure to explain which equation represents which situation. (b) Find the cost of each type of cookie. Show your work. (c) Explain which method you used to solve the system and why you chose that method.

a) [tex]25m+30c=221.25\\5m+45c=191.25[/tex]
b) Cost of a macadamia nut chip cookie is $4.32 and the cost of triple chocolate cookie. is $3.77
c) We use elimination method since it helps us to eliminate one of the variables.

Step-by-step explanation:

Let m be the cost of macadamia nut chip cookie and c be the cost of triple chocolate cookie.

Then according to the question we have the following equations:-

[tex]25m+30c=221.25....(1)\\5m+45c=191.25...(2)[/tex]

Multiplying 5 on both sides of the equation (2), we get

[tex]25m+225c=956.25......(3)[/tex]

By using elimination method, subtract equation (1) from (3) we get

[tex]195c=735\\\Rightarrow\ c=3.77[/tex]

Substitute the value of c in (2), we get

[tex]5m+45(3.77)=191.25\\\Rightarrow\ m=4.32[/tex]