To solve the problem, we need to determine which of the given ordered pairs, [tex]\((4, 1)\)[/tex] or [tex]\((1, 4)\)[/tex], satisfy the constraints:
1. The total number of snacks (hot dogs and peanuts) should be at least 4.
2. The total cost of the snacks should not exceed \[tex]$7.
Let's check each pair one by one.
### Checking the Pair \((4, 1)\)
1. Total Number of Snacks:
\[
x + y \geq 4
\]
Plugging in the values \(x = 4\) and \(y = 1\):
\[
4 + 1 = 5 \geq 4
\]
This satisfies the first condition.
2. Total Cost:
\[
2x + y \leq 7
\]
Plugging in the values \(x = 4\) and \(y = 1\):
\[
2 \cdot 4 + 1 = 8 + 1 = 9 \leq 7
\]
This does not satisfy the second condition.
The pair \((4, 1)\) satisfies the first condition but does not satisfy the second condition.
### Checking the Pair \((1, 4)\)
1. Total Number of Snacks:
\[
x + y \geq 4
\]
Plugging in the values \(x = 1\) and \(y = 4\):
\[
1 + 4 = 5 \geq 4
\]
This satisfies the first condition.
2. Total Cost:
\[
2x + y \leq 7
\]
Plugging in the values \(x = 1\) and \(y = 4\):
\[
2 \cdot 1 + 4 = 2 + 4 = 6 \leq 7
\]
This satisfies the second condition.
The pair \((1, 4)\) satisfies both conditions.
### Conclusion
The ordered pair \((1, 4)\) is a solution that satisfies both constraints:
1. The total number of snacks is at least 4.
2. The total cost does not exceed \$[/tex]7.
