A store sells dog bowls for $6 and $8. A kennel owner wants to spend at least $24 but no more than $48 on dog bowls. Find the system of inequalities.

$\begin{array}{l}
8 x+6 y \leq 24 \\
8 x+6 y \leq 48
\end{array}$

$\begin{array}{l}
6 x+8 y \geq 24 \\
6 x+8 y \leq 48
\end{array}$

$\begin{array}{l}
6 x-8 y \geq 24 \\
6 x+8 y \leq 48
\end{array}$

$\begin{array}{l}
8 x+8 y \geq 24 \\
6 x+6 y \leq 48
\end{array}$

The system of inequalities is 6 x + 8 y ≥ 24 6 x + 8 y ≤ 48 ​ ​

Explanation

Formulating the Inequalities Let x be the number of $6 dog bowls and y be the number of $8 dog bowls. The total cost of the dog bowls is 6 x + 8 y . The kennel owner wants to spend at least $24, so 6 x + 8 y ≥ 24 . The kennel owner wants to spend no more than $48, so 6 x + 8 y ≤ 48 . The system of inequalities is 6 x + 8 y ≥ 24 and 6 x + 8 y ≤ 48 .

Determining the System of Inequalities The problem states that a store sells dog bowls for $6 and $8. A kennel owner wants to spend at least $24 but no more than $48 on dog bowls. We need to find the system of inequalities that represents this situation. Let x be the number of $6 dog bowls and y be the number of $8 dog bowls. The total cost of the dog bowls is given by the expression 6 x + 8 y . Since the kennel owner wants to spend at least $24, we have the inequality 6 x + 8 y ≥ 24 . Also, the kennel owner wants to spend no more than $48, so we have the inequality 6 x + 8 y ≤ 48 . Therefore, the system of inequalities that represents this situation is:


6 x + 8 y ≥ 24
6 x + 8 y ≤ 48

Identifying the Correct Option Comparing the derived system of inequalities with the given options, we can see that the correct option is:

6 x + 8 y ≥ 24
6 x + 8 y ≤ 48
Examples
Imagine you're planning a party and need to buy snacks. Some snacks cost $6 each, and others cost $8 each. You want to spend at least $24 but no more than $48. Setting up a system of inequalities helps you figure out how many of each snack you can buy within your budget. This is similar to the dog bowl problem, where you're trying to find the possible combinations of dog bowls you can buy within a certain price range. Understanding how to set up and solve these inequalities can help you make informed decisions when budgeting for various items.

Answered by GinnyAnswer | 2025-07-03

The correct system of inequalities for the kennel owner's budget is 6 x + 8 y ≥ 24 and 6 x + 8 y ≤ 48 . This represents the conditions that the owner must spend at least $24 but no more than $48 on dog bowls. Therefore, the selected option is 6 x + 8 y ≥ 24 and 6 x + 8 y ≤ 48 .
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Answered by Anonymous | 2025-07-04