jace is buying cookies and brownies for a party. he needs at least 8 cookies and at least 4 brownies. a cookies costs $3 and a brownies costs $5. the most he can spend is 60$.

Question

a. create a system of linear ineqaulites in 2 variables from the description, define your variables.

Answer 1

To create a system of linear inequalities from the given situation, we first need to define our variables:

Let:

• \( c \) = number of cookies
• \( b \) = number of brownies

Now, based on the requirements and constraints presented in the problem, we can form the following inequalities:

1. Minimum cookie requirement: Jace needs at least 8 cookies. \[ c \geq 8 \]

2. Minimum brownie requirement: Jace needs at least 4 brownies. \[ b \geq 4 \]

3. Cost constraint: A cookie costs $3 and a brownie costs $5, and Jace has a maximum budget of $60. The total cost can be expressed as: \[ 3c + 5b \leq 60 \]

Putting it all together, the system of linear inequalities is:

\[ \begin{align*} c & \geq 8 \quad \text{(minimum cookies)} \ b & \geq 4 \quad \text{(minimum brownies)} \ 3c + 5b & \leq 60 \quad \text{(budget constraint)} \end{align*} \]

This system represents the constraints that Jace faces while planning his purchases for the party.