Question

Devine goes to the store with a $20 bill to buy some oranges. The oranges cost $2.50 per round. Which inequality represents all possible values of p, the number of pounds of oranges Devin can nut at the store with his money?
Use the number line below to represent the solution.
—————————————————
0 1 2 3 4 5 6 7 8 9

Answer 1

To determine the inequality that represents all possible values of \( p \) (the number of pounds of oranges Devine can buy with the $20 bill), we start by considering the cost of the oranges per pound.

Given:
- The cost of oranges is $2.50 per pound.
- Devine has $20 to spend.

The total cost for \( p \) pounds of oranges can be represented as:

\[
\text{Total Cost} = 2.50p
\]

To stay within the budget, the total cost must be less than or equal to $20:

\[
2.50p \leq 20
\]

Now, to solve for \( p \), we can divide both sides of the inequality by 2.50:

\[
p \leq \frac{20}{2.50}
\]

Calculating the right side:

\[
\frac{20}{2.50} = 8
\]

Thus, the inequality that represents all possible values of \( p \) is:

\[
p \leq 8
\]

In words, Devine can purchase a maximum of 8 pounds of oranges.

### Number Line Representation

To visually represent this inequality on the number line, mark a closed dot at 8 (indicating that Devine can buy exactly 8 pounds) and shade to the left of 8 to indicate all values less than or equal to 8.

```
0 1 2 3 4 5 6 7 8 9
------------(================
```

In this representation, the parenthesis or closed dot indicates that 8 is included, while the shading to the left shows all possible values of \( p \) (from 0 to 8).