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: $$\begin{array}{rlr}6x+5y& =38\text{(1)}2x+3y& =18\text{(2)}\end{array}$$