Benson's Bakery Cookie Pricing Dilemma

What is the cost of a dozen chocolate cookies and a dozen oatmeal cookies at Benson's Bakery?

a) Let C be the cost of a dozen chocolate cookies, and O be the cost of a dozen oatmeal cookies. 3C + 1O = 29 2C + 9O = 86

Answer:

This problem involves setting up and solving systems of linear equations. By doing so, we find that a dozen oatmeal cookies cost $8 and a dozen chocolate cookies cost $7.

Explanation:

In this problem, Benson's Bakery sold different quantities of chocolate and oatmeal cookies to two customers at varying prices. To determine the cost of a dozen chocolate cookies (C) and a dozen oatmeal cookies (O), we need to set up a system of equations based on the information given.

The first equation represents the cookies sold to the first customer: 3C + 1O = 29. The second equation represents the cookies sold to the second customer: 2C + 9O = 86.

To solve for O and C, we can use the method of elimination. By multiplying the first equation by 2 and the second equation by 3, we get 6C + 2O = 58 and 6C + 27O = 258. Subtracting the former from the latter gives us 25O = 200. Therefore, a dozen oatmeal cookies cost $8.

Substitute O = 8 into the first equation, 3C + 8 = 29, we can solve for C and find that a dozen chocolate cookies cost $7.

By solving the system of equations, we have determined that a dozen chocolate cookies cost $7, and a dozen oatmeal cookies cost $8 at Benson's Bakery.