Betty bought 6 cookies and 5 brownies for a total of $38. Duncan bought 2 cookies and 3 brownies for a total of $18. Which is the system of equations that could be used to solve for the price of a cookie and the price of a brownie? Assume a cookie's price is xx and a brownie's price is yy.

Question

Answer
Attempt 1 out of 3

Equation representing Betty's purchase:

Equation representing Duncan's purchase:

Answer 1

To represent the problem with a system of equations, we can define the variables as follows:

• Let \( x \) be the price of a cookie.
• Let \( y \) be the price of a brownie.

Now we can set up the equations based on the information given in the problem:

1. Betty's Purchase: Betty bought 6 cookies and 5 brownies for a total of $38. This can be represented by the equation: \[ 6x + 5y = 38 \]

2. Duncan's Purchase: Duncan bought 2 cookies and 3 brownies for a total of $18. This can be represented by the equation: \[ 2x + 3y = 18 \]

So, the system of equations is: \[ \begin{align*} 6x + 5y &= 38 \quad \text{(1)} \ 2x + 3y &= 18 \quad \text{(2)} \end{align*} \]