Mrs. Julien2019s And Mrs. Castillejo2019s Classes Are Selling Cookie Dough For A School Fundraiser. Customers Can Buy Packages Of Macadamia Nut Chip C

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.
Answer:

 

Answer:

a) The system of equations are:

Mrs. Juliens class: 25m + 30t= $221.25 (equation 1)

Mrs. Castillejos class: 5m + 45t=$191.25 (equation 2)

Note: For more elaborate explanation, refer to Step 2 below.

b) Cost of each type of cookie:

Price of macadamia nut chip cookie dough= $4.33

Price of triple chocolate cookie dough=$3.77

Note: For more elaborate explanation, refer to Step 3 to 4 below.

c) Explain which method is used to solve the system

Elimination is used in solving the system. It is easier to use in this given as "25 m and 5m" can be easily eliminated since only one of the equations needs to be multiplied with a certain factor. Both sides of equation 2 will be multiplied to 5 to eliminate "25m" which then makes it possible to solve for t. Once there is already a value of t, m can be solved through substitution in either of the equations.

Step-by-step explanation:

Step 1: Assigning variables.

Let: macadamia nut chip cookie dough = m

       triple chocolate cookie dough= t

Step 2: Write the system of equations

Mrs. Juliens class sold the following:

1. 25 macadamia nut chip cookie dough (represented as 25m)
2. 30 triple chocolate cookie dough (represented as 30t)
3. Total of $221.25

Interpretation: 25m + 30t= $221.25 (equation 1)

Mrs. Castillejos class sold the following:

1. 5 macadamia nut chip cookie dough (represented as 25m)
2. 45 triple chocolate cookie dough (represented as 30t)
3. Total of $191.25

Interpretation: 5m + 45t=$191.25 (equation 2)

Step 3: Solve the system of equations through elimination

I will use elimination for this problem. It will be easy to eliminate the "5m" of equation 2 (macadamia nut chip cookie dough sold by Mrs. Castillejos class) since "25m" of equation 1 is divisible to it. After eliminating this, then I can now solve for the price of "t" or triple chocolate cookie dough.

1. Multiply both sides of equation 2  to 5 so that the coefficient of m for both equation 1 and 2 will be the same. Equation 2 will now be equal to: 25m + 225t=$956.25
2. Get the difference of equation 1 and 2. The answer will be: 225t-30t=956.25-221.25
3. Simplify: 195t=735
4. Solve for t: t=$3.77

Step 4: Substitute value of t to either of the equations to find the value of m

1. Substitute to Equation 1: 25m + (30)(3.77)=221.25
2. Solve for m: m=$4.33