IDNLearn.com: Your trusted source for finding accurate and reliable answers. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
Sagot :
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].
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].
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.