Question

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 $5. the most he can spend is 60$.
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.