https://file.aiquickdraw.com/mathbot/file/1726759922900j3nuolex.jpg

Mrs. Martin has $50 to spend on sweet (x) and sour (y) candy. Each package of sweet candy costs $3, and each package of sour candy costs $5. She also needs to buy at least 8 packages of candy in total.

The key elements of the problem:
1. The cost equation: $ 3x + 5y \leq 50 $, since the total amount spent should be less than or equal to $50.
2. The minimum package requirement: $ x + y \geq 8 $, since Mrs. Martin needs to buy at least 8 packages.

Given this, the system of inequalities should reflect:
\[
\begin{cases}
x + y \geq 8 \\
3x + 5y \leq 50
\end{cases}
\]

Now, let's review the options in the image:
1. $ x + y \leq 83x + 5y \geq 50 $ — incorrect.
2. $ x + y \geq 83x + 5y \geq 50 $ — incorrect.
3. $ x + y \leq 85x + 3y \leq 50 $ — incorrect.
4. $ x + y \geq 85x + 3y \leq 50 $ — **correct**.

So, the correct choice is the last one. Would you like further details or have any questions?

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Here are 5 related questions:
1. How do you solve systems of inequalities graphically?
2. How would the problem change if Mrs. Martin had a different budget?
3. What is the role of constraints in real-life optimization problems?
4. How can we determine the maximum or minimum number of each type of candy she could buy?
5. How do linear inequalities differ from linear equations?

**Tip:** Always remember to identify key variables and constraints before forming equations in word problems.

Mrs. Martin has $50 to spend on sweet and sour candy for a school party. She knows she needs to buy at least 8 packages of sweet and sour candy. Each package of sweet candy, x, costs $3, and each package of sour candy, y, costs $5. Which system of inequalities can be used to determine how many packages of each type of candy Mrs. Martin can buy?

Learn how to determine the system of inequalities for a candy budgeting problem where Mrs. Martin has $50 to spend on sweet and sour candies, with each package costing $3 and $5 respectively. The solution involves setting up and solving linear inequalities.

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