Math Problem Statement

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?

Solution

To solve this problem, we need to set up inequalities based on the given information:

  1. Total weight requirement: Amy needs at least 5 pounds of fruit.

    • This can be written as: x+y5x + y \geq 5 where xx represents the pounds of watermelon, and yy represents the pounds of bananas.
  2. Budget constraint: Amy has a maximum of $25 to spend.

    • Since watermelon costs $2.25 per pound and bananas cost $1.50 per pound, the total cost must satisfy: 2.25x+1.50y252.25x + 1.50y \leq 25

Now, we match this system of inequalities to the answer choices.

Correct Answer: D
Explanation:

  • x+y5x + y \geq 5 (minimum weight requirement)
  • 2.25x+1.50y252.25x + 1.50y \leq 25 (cost constraint)

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Related Questions

  1. How would the solution change if Amy had a budget of $30 instead of $25?
  2. What would happen if bananas cost $2.00 per pound instead of $1.50?
  3. Can you solve for the maximum amount of watermelon Amy could buy within the budget?
  4. How would the inequalities change if Amy needed exactly 5 pounds of fruit?
  5. What if watermelon and bananas had to be bought in whole pounds?

Tip

When setting up inequalities, always define each variable and make sure the inequality matches the conditions of the problem (such as minimum/maximum constraints).

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Systems of Inequalities

Formulas

x + y ≥ 5 (minimum weight requirement)
2.25x + 1.50y ≤ 25 (budget constraint)

Theorems

Properties of inequalities

Suitable Grade Level

Grade 8-10