1. 
Amy is making a fruit salad for a potluck at work. She can spend at most $25 on fruit. Watermelon costs 2.25 per pound and bananas cost 1.50 per pound. She will need at least 5 pounds of fruit for her salad.

Which system of inequalities can be used to determine the pounds of watermelon, x, and the pounds of bananas, y, Amy bought?
A.x + y > 5
2.25x + 1.50y < 25
B.x + y ≥ 25
2.25x + 1.50y ≤ 5
C.x + y ≥ 5
1.50x + 2.25y ≤ 25
D.x + y ≥ 5
2.25x + 1.50y ≤ 25

To determine the correct system of inequalities, let's break down the problem step by step:

1. **Budget Constraint**: Amy can spend **at most $25** on the fruit. This suggests that the total cost of watermelon and bananas combined must be **less than or equal to $25**. Since watermelon costs $2.25 per pound and bananas cost $1.50 per pound, the inequality for this constraint is:
   \[
   2.25x + 1.50y \leq 25
   \]

2. **Minimum Weight Requirement**: Amy needs **at least 5 pounds** of fruit in total. This implies that the sum of the pounds of watermelon ($x$) and bananas ($y$) should be **greater than or equal to 5 pounds**. Thus, the inequality for this requirement is:
   \[
   x + y \geq 5
   \]

Now, comparing these inequalities with the answer choices:

- **Option D** matches our derived inequalities: 
  \[
  x + y \geq 5
  \]
  \[
  2.25x + 1.50y \leq 25
  \]

### Correct Answer:
**D.** $ x + y \geq 5 $ and $ 2.25x + 1.50y \leq 25 $

Would you like further explanation, or have any questions?

---

1. How would the solution change if Amy's budget increased to $30?
2. What would happen if the minimum fruit requirement was 8 pounds instead of 5?
3. How would Amy's choices change if both fruits were priced equally?
4. Can you graph the inequalities for a visual solution?
5. What if bananas were more expensive than watermelon, how would that affect the system?

**Tip:** When solving inequalities, identify constraints individually to build a clear system.

Amy is making a fruit salad for a potluck at work. She can spend at most $25 on fruit. Watermelon costs 2.25 per pound and bananas cost 1.50 per pound. She will need at least 5 pounds of fruit for her salad. Which system of inequalities can be used to determine the pounds of watermelon, x, and the pounds of bananas, y, Amy bought? A.x + y > 5 2.25x + 1.50y < 25 B.x + y ≥ 25 2.25x + 1.50y ≤ 5 C.x + y ≥ 5 1.50x + 2.25y ≤ 25 D.x + y ≥ 5 2.25x + 1.50y ≤ 25

Determine the correct system of inequalities for Amy’s fruit salad budget and weight requirements. This problem involves setting up and solving inequalities to satisfy both budget (maximum $25) and weight (minimum 5 pounds) constraints, with costs of $2.25 per pound for watermelon and $1.50 per pound for bananas. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation