Question

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 $112.50. Mrs. Castillejo’s class sold 8 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $124.50

(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.

Answer 1

Answer: the cost of one package of macadamia nut chip cookie dough is $1.5

the cost of one package of triple chocolate cookie dough is $2.5

Explanation:

Let x represent the cost of one package of macadamia nut chip cookie dough.

Let y represent the cost of one package 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 $112.50. This means that

25x + 30y = 112.5 - - - - - - - - - - - - -1

Mrs. Castillejo’s class sold 8 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $124.50. This means that

8x + 45y = 124.5 - - - - - - - - - - -2

Multiplying equation 1 by 8 and equation 2 by 25, it becomes

200x + 240y = 900

200x + 1125 = 3112.5

Subtracting, it becomes

- 885y = - 2212.5

y = - 2212.5/- 885

y = 2.5

Substituting y = 2.5 into equation 1, it becomes

25x + 30 × 2.5 = 112.5

25x + 75 = 112.5

25x = 112.5 - 75 = 37.5

x = 37.5/25 = 1.5

The method used is the elimination method. It is more convenient to use.