Question

Question 1Identify the inequality that represents the situation. Jason has $20 to spend at Sonic. He wants a large blue raspberry slush which costs $8. He also wants some mozzarella sticks which cost $2 each. How many mozzarella sticks can he purchase? Responses8m + 2 ≤ 208m + 2 ≤ 202m + 8 ≤202m + 8 ≤202m + 8 ≥ 202m + 8 ≥ 208m + 2 ≥ 208m + 2 ≥ 20Question 2Graph the solution to the inequality.

Answer 1

To solve the problem, we first need to set up the inequality that represents Jason's spending situation.

Question 1: Identify the inequality

1. Jason's total budget: $20
2. Cost of a large blue raspberry slush: $8
3. Cost of mozzarella sticks: $2 each

Let \( m \) represent the number of mozzarella sticks Jason wants to buy.

The total cost \( C \) of the items he wants to purchase can be expressed as:

\[ C = 8 + 2m \]

Since he cannot spend more than $20, we can set up the following inequality:

\[ 8 + 2m \leq 20 \]

To isolate \( m \), subtract 8 from both sides:

\[ 2m \leq 12 \]

Now, divide both sides by 2:

\[ m \leq 6 \]

Thus, the correct inequality that represents the situation is:

\[ 2m + 8 \leq 20 \]

Question 2: Graph the solution to the inequality

To graph the solution \( m \leq 6 \):

• X-axis: represents the number of mozzarella sticks \( m \).
• Y-axis: would not be needed for this inequality, as we are only focusing on the x-values.

1. Draw a number line (horizontal line).
2. Mark the value 6 on the number line.
3. Since the inequality is \( m \leq 6\), you would:
   • Fill in or shade the point at 6 (to indicate that 6 is included).
   • Shade to the left of 6 (to indicate all values less than 6 are included).

This visually represents that Jason can buy 0 to 6 mozzarella sticks, inclusive.