Let's consider Cody's requirements and the options available. Cody has a budget of \[tex]$7. He needs to buy at least 4 snacks comprising hot dogs and peanuts where hot dogs cost \$[/tex]2 each and peanuts cost \[tex]$1 each.
We are given the following constraints:
1. \( x + y \geq 4 \) (Cody needs at least 4 snacks)
2. \( 2x + y \leq 7 \) (Cody's total expenditure should not exceed \$[/tex]7)
We need to evaluate which ordered pair, [tex]\((1, 1)\)[/tex] or [tex]\((1, 3)\)[/tex], satisfies both of these conditions.
### Option 1: [tex]\((1, 1)\)[/tex]
1. Number of Snacks Constraint:
[tex]\[
x + y = 1 + 1 = 2
\][/tex]
This does not meet the requirement of having at least 4 snacks since [tex]\(2 < 4\)[/tex].
Since the first condition is not satisfied, [tex]\((1,1)\)[/tex] is not a suitable solution regardless of the cost.
### Option 2: [tex]\((1, 3)\)[/tex]
1. Number of Snacks Constraint:
[tex]\[
x + y = 1 + 3 = 4
\][/tex]
This meets the condition [tex]\( x + y \geq 4 \)[/tex].
2. Cost Constraint:
[tex]\[
2x + y = 2(1) + 3 = 2 + 3 = 5
\][/tex]
This satisfies the condition [tex]\( 2x + y \leq 7 \)[/tex] since [tex]\( 5 \leq 7 \)[/tex].
### Conclusion
The ordered pair [tex]\((1,3)\)[/tex] satisfies both conditions:
1. [tex]\( x + y = 4 \geq 4 \)[/tex]
2. [tex]\( 2x + y = 5 \leq 7 \)[/tex]
Thus, the correct ordered pair that is a solution to Cody's problem is [tex]\((1,3)\)[/tex].
