Question

A pack of paper costs $3.79, including tax. Mr. Valentino wants to purchase packs of paper for his class and has a $15 budget. Write and solve an inequality to solve for the number of packs of paper Mr. Valentino can purchase, and describe the graph of the solution.

Answer 1

Let's denote the number of packs of paper Mr. Valentino can purchase as \( x \).

The cost per pack of paper is $3.79. Given that Mr. Valentino has a budget of $15, we need to write an inequality that represents the total cost of \( x \) packs of paper being less than or equal to $15.

The inequality will be:
\[ 3.79x \leq 15 \]

To solve for \( x \), divide both sides of the inequality by the cost per pack, which is 3.79:
\[ x \leq \frac{15}{3.79} \]

Now, let's calculate \( \frac{15}{3.79} \):

\[ x \leq 3.96 \]

Since Mr. Valentino can only purchase a whole number of packs, we need to round down 3.96 to the nearest whole number. Thus:
\[ x \leq 3 \]

Therefore, Mr. Valentino can purchase at most 3 packs of paper.

To describe the graph of the solution:

- The graph will be on a number line.
- Since \( x \) represents the number of packs and must be a whole number, the potential values are non-negative integers.
- The solution includes \( x = 0, 1, 2, \) or \( 3 \).

On the number line:

1. Draw a line and label points corresponding to 0, 1, 2, 3, 4, etc.
2. Place a closed circle (to indicate inclusion) on 0, 1, 2, and 3.
3. Shade the line or place points at these numbers indicating that these are the possible numbers of packs Mr. Valentino can purchase within his budget.

Thus, the graphical representation on the number line will look as follows:

```
---|---|---|---|---
0 1 2 3 4 ...
```