Let's analyze the given problem and break it down into the necessary inequalities:
1. Budget Constraint:
Laura has a budget of [tex]$50. The cost of one stuffed animal is $[/tex]6, and the cost of one toy truck is $4. If [tex]\(x\)[/tex] represents the number of stuffed animals and [tex]\(y\)[/tex] represents the number of toy trucks, then the total cost of party favors can be expressed as [tex]\(6x + 4y\)[/tex]. This total cost should not exceed Laura's budget:
[tex]\[
6x + 4y \leq 50
\][/tex]
2. Guest Constraint:
Laura wants to provide one party favor per person to at least 10 guests. Therefore, the total number of party favors, represented by [tex]\(x + y\)[/tex], must be at least 10:
[tex]\[
x + y \geq 10
\][/tex]
Combining these constraints, we get the following system of inequalities:
[tex]\[
\begin{cases}
6x + 4y \leq 50 \\
x + y \geq 10
\end{cases}
\][/tex]
This matches with option B:
[tex]\[
\begin{cases}
6x + 4y \leq 50 \\
x + y \geq 10
\end{cases}
\][/tex]
Therefore, the correct answer is B.
