Question

JarJar Binks purchased 12 boxes of Thin Mints cookies and 12 boxes of Peanut Butter Patty cookies, for a total of $156. Later, they had to order 4 more boxes of Thin Mints cookies and 6 more Peanut Butter Patty cookies for a total of $62.

The system of equations that can be used to find m, the cost each box of Thin Mints cookies, and p, the cost of each box of Peanut Butter Patty cookies, is shown.

12m + 12p = 156

4m + 6p = 62

What is the cost of each box of Thin Mints cookies (m)?

a) $6

b) $5

c) $4

d) $3

Answer 1

After simplifying and solving the provided system of equations, the cost of each box of Thin Mints cookies (m) is determined to be $8, which is not among the provided choices.

Step-by-step explanation:

To determine the cost of each box of Thin Mints cookies (marked as m) and each box of Peanut Butter Patty cookies (marked as p), we need to solve the system of equations:

1. 12m + 12p = 156
2. 4m + 6p = 62

First, we can simplify both equations by dividing the coefficients by their greatest common divisor. For the first equation, we divide by 12 and for the second, by 2:

1. m + p = 13
2. 2m + 3p = 31

To eliminate one of the variables, we can multiply the first equation by 2:

1. 2m + 2p = 26

Now subtract the first equation from the second equation:

1. (2m + 3p) - (2m + 2p) = 31 - 26
2. 3p - 2p = 31 - 26
3. p = 5

We now substitute the value of p back into the first equation:

1. m + 5 = 13
2. m = 13 - 5
3. m = 8

Since the cost of each box of Thin Mints cookies is $8, none of the options (a) $6, (b) $5, (c) $4, or (d) $3 are correct. Thus, the correct answer is not listed among the provided choices.