Question

tanner saved $350 this summer. he plans to spend some of the money on art sup and some on video games. let v represent the money, in dollars, tanner plans to spend on video games. which inequality models the story? \\( v > 350 \\) \\( v \geq 350 \\) \\( v < 350 \\) \\( v \leq 350 \\) graph the inequality that models the story. to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it. 200 225 250 275 300 325 350 375 400 425 450

Explanation:

Part 1: Choosing the Correct Inequality

Step 1: Analyze the Total Savings

Tanner has saved $350. He will spend some on video games (represented by LXI0) and some on art supplies. So the money spent on video games (LXI1) can be at most $350 (since he can't spend more than he saved, and he can spend all of it on video games if he wants to spend nothing on art supplies).

Step 2: Evaluate the Inequalities

• \( v > 350 \): This would mean he spends more than $350, which is impossible because he only has $350. Eliminate this.
• \( v \geq 350 \): This means he spends $350 or more, which is also impossible. Eliminate this.
• \( v < 350 \): This means he spends less than $350, but he could also spend exactly $350 (if he spends nothing on art supplies). So this is too restrictive. Eliminate this.
• \( v \leq 350 \): This means he spends $350 or less, which matches the situation (he can spend from $0 up to $350 on video games, since the rest will go to art supplies or he can spend all on video games).

Step 1: Identify the Endpoint

The inequality is \( v \leq 350 \), so the endpoint is at \( v = 350 \). Since the inequality is "less than or equal to", the endpoint is a closed circle (to include 350).

Step 2: Determine the Direction of the Ray

We need to show all values of \( v \) that are less than or equal to 350. So the ray should start at 350 (closed circle) and go to the left (towards smaller numbers) because we want values less than 350 as well as 350 itself.

Graph Description:

• Plot a closed circle at 350 on the number line.
• Draw a ray starting at 350 and extending to the left (towards 325, 300, etc.).

(Note: Since we can't draw the graph here, but the steps are: place a closed dot at 350 and draw an arrow pointing to the left along the number line.)

Answer:

(for the inequality part):
\( v \leq 350 \)

Part 2: Graphing the Inequality \( v \leq 350 \)