Question

Antoine has $18.20 to spend on some oranges and a pumpkin. Oranges cost $1.30 per pound, and a pumpkin costs $5.20.

Which inequality models this situation, where x is the number of pounds of oranges? Select the correct inequality.

Solve the inequality. How many pounds of oranges can Antoine buy? Select BOTH correct answers.

Group of answer choices

1.30x + 5.20 ≤ 18.20

x ≤ 3; Antoine can buy 3 pounds or less of oranges.

x ≤ 10; Antoine can buy 10 pounds or less of oranges.

5.20x + 1.30 ≤ 18.20

Answer 1

To model the situation where Antoine has $18.20 to spend on oranges and a pumpkin, let \( x \) represent the number of pounds of oranges he buys. The cost of oranges is $1.30 per pound, and the pumpkin costs $5.20. Therefore, the total cost for oranges and the pumpkin can be represented as follows:

\[
1.30x + 5.20 \leq 18.20
\]

This inequality states that the total cost of the oranges (1.30x) plus the cost of the pumpkin (5.20) must be less than or equal to his total available amount ($18.20).

Now let's solve the inequality:

1. Start with the inequality:
\[
1.30x + 5.20 \leq 18.20
\]

2. Subtract 5.20 from both sides:
\[
1.30x \leq 18.20 - 5.20
\]

3. Simplify the right side:
\[
1.30x \leq 13.00
\]

4. Divide both sides by 1.30 to isolate \( x \):
\[
x \leq \frac{13.00}{1.30}
\]

5. Perform the division:
\[
x \leq 10
\]

This means Antoine can buy **10 pounds or less** of oranges.

### Summary of Correct Answers:
- The correct inequality is: **1.30x + 5.20 ≤ 18.20**
- The solution to the inequality indicates: **x ≤ 10; Antoine can buy 10 pounds or less of oranges.**