Question
Devon goes to the store with a 20$ bill to buy some oranges the oranges cost 2.50$ per pound which inequality represents all possible values of p, the number of pounds of oranges Devon can buy at the store with his money use the number line below to represent the solution 0 to 9
Answers
GPT-4o mini
To write the inequality that represents all possible values of \( p \), the number of pounds of oranges Devon can buy, we need to consider how much money he has and how much the oranges cost.
Devon has $20, and the cost of oranges is $2.50 per pound. The total cost for \( p \) pounds of oranges will be \( 2.50p \). Since he cannot spend more than $20, we can set up the following inequality:
\[
2.50p \leq 20
\]
To solve for \( p \), we divide both sides by 2.50:
\[
p \leq \frac{20}{2.50}
\]
\[
p \leq 8
\]
This means Devon can buy up to 8 pounds of oranges. Since \( p \) must also be a non-negative number, we express the solution as:
\[
0 \leq p \leq 8
\]
To represent this on a number line from 0 to 9, we can mark the range of pounds of oranges Devon can buy:
1. Draw a number line from 0 to 9.
2. Shade the area from 0 to 8.
3. Use a closed circle at 0 and an open circle at 9 (indicating 9 is not included) to represent that \( p \) can be any value from 0 to 8, inclusive.
Here is a description of how it will look:
```
0 1 2 3 4 5 6 7 8 9
-----|---|---|---|---|---|---|---|---|---|-----
●=================================○
```
- The line between the points shows that all values between 0 and 8 are included (inclusive of 0 and exclusive of 9).
Devon has $20, and the cost of oranges is $2.50 per pound. The total cost for \( p \) pounds of oranges will be \( 2.50p \). Since he cannot spend more than $20, we can set up the following inequality:
\[
2.50p \leq 20
\]
To solve for \( p \), we divide both sides by 2.50:
\[
p \leq \frac{20}{2.50}
\]
\[
p \leq 8
\]
This means Devon can buy up to 8 pounds of oranges. Since \( p \) must also be a non-negative number, we express the solution as:
\[
0 \leq p \leq 8
\]
To represent this on a number line from 0 to 9, we can mark the range of pounds of oranges Devon can buy:
1. Draw a number line from 0 to 9.
2. Shade the area from 0 to 8.
3. Use a closed circle at 0 and an open circle at 9 (indicating 9 is not included) to represent that \( p \) can be any value from 0 to 8, inclusive.
Here is a description of how it will look:
```
0 1 2 3 4 5 6 7 8 9
-----|---|---|---|---|---|---|---|---|---|-----
●=================================○
```
- The line between the points shows that all values between 0 and 8 are included (inclusive of 0 and exclusive of 9).