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A summer camp cookout is planned for the campers and their families. There is room for 450 people. Each adult costs \[tex]$7, and each camper costs \$[/tex]4. There is a maximum budget of \$1,150. Write the system of inequalities to represent this real-world scenario, where [tex]\( x \)[/tex] is the number of adults and [tex]\( y \)[/tex] is the number of campers.

[tex]\[
\begin{array}{l}
x + y \leq 450 \\
7x + 4y \leq 1,150
\end{array}
\][/tex]



Answer :

GinnyAnswer
To represent the scenario of planning a summer camp cookout with a system of inequalities, we need to consider two main constraints: the room capacity and the budget.

1. Room Capacity Constraint:
- The total number of people (adults [tex]\( x \)[/tex] and campers [tex]\( y \)[/tex]) that can be accommodated is at most 450.
- This can be represented by the inequality:
[tex]\[ x + y \leq 450 \][/tex]

2. Budget Constraint:
- Each adult costs \[tex]$7, and each camper costs \$[/tex]4.
- The total cost for the adults and campers must not exceed \$1150.
- This can be represented by the inequality:
[tex]\[ 7x + 4y \leq 1150 \][/tex]

Putting these constraints together, the system of inequalities that represents this scenario is:

[tex]\[ \begin{cases} x + y \leq 450 \\ 7x + 4y \leq 1150 \end{cases} \][/tex]

These inequalities ensure that both the room capacity and the budget constraints are satisfied for the camp cookout.

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