To find the number of packs of paper Mr. Valentino can purchase within his $20 budget, we can use an inequality.
Let's assume that Mr. Valentino can buy "p" packs of paper.
The cost of one pack of paper, including tax, is $3.75. So, the total cost of "p" packs of paper can be calculated as 3.75p.
We want the total cost to be less than or equal to Mr. Valentino's budget of $20. Therefore, we can write the inequality as:
3.75p ≤ 20
To solve this inequality, we can divide both sides by 3.75 to isolate "p".
3.75p / 3.75 ≤ 20 / 3.75
Simplifying, we have:
p ≤ 5.333333...
Since "p" represents the number of packs of paper, we need to find the maximum number of packs he can buy.
Since "p" must be less than or equal to 5.333..., we round down to the nearest whole number to get the maximum number of packs he can buy.
Therefore, Mr. Valentino can purchase no more than 5 packs of paper within his $20 budget.
The graph of this solution can be represented by the function f(p) = 3.75p, where "p" is an integer from 0 to 5. This means that the graph will show the values of "p" from 0 to 5 on the x-axis, and the corresponding values of 3.75p on the y-axis. Each point on the graph will represent a possible number of packs Mr. Valentino can purchase within his budget